MOST-ESSENTIAL-LEARNING-COMPETENCIES-IN-MATHEMATICS (1).pdf

Department of Education  Most Essential Learning Competencies in Mathematics THIS IS NOT FOR SALE
1
MOST
ESSENTIAL
LEARNING
COMPETENCIES IN
MATHEMATICS
CONTENTS
Preliminary Page Grade 1 to 10 Page Senior High School Page
Briefer 2 Grade 1 7 General Mathematics 61
Grade 2 11 Statistics and Probability 65
Grade 3 17 Business Mathematics 69
Grade 4 24 Basic Calculus 73
Grade 5 30 Pre-Calculus 75
Grade 6 37
Grade 7 44
Grade 8 48
Grade 9 53
Grade 10 57

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Guiding our Teachers: A Briefer on Using The Math MELCs
Identifying the learning competencies in the Mathematics K to 10 Curriculum that satisfy the criterion endurance posits that these most
essential learning competencies necessitates the realization of the twin goals of Mathematics – problem solving and critical thinking.
Laying the foundational concepts and skills at each grade level are pivotal in the learning progression of each child. This consequently
scaffold the learner’s understanding and acquisition of higher skills.
The identified most essential learning competencies in Math puts premium on the development of numeracy skills which are fundamental
to practical and real-life problems, rather than Math content-knowledge; and on the development of higher-order thinking skills which
goes beyond procedural fluency. It followed the content domains as articulated in the curriculum – Numbers and Number Sense,
Measurement, Geometry, Patterns and Algebra, and Statistics and Probability.
Similarly, the skills and processes to be developed as emphasized in the curriculum, are maintained. These include knowing and
understanding; estimating, computing and solving; visualizing and modelling, representing and communicating, conjecturing, reasoning,
proving and decision-making; and applying and connecting.
It is further aimed that the values and attitudes – accuracy, creativity, objectivity, perseverance, and productivity, be strongly honed
among learners especially at this crucial time of health emergencies. The use of various instructional resources, especially calculators,
computers, smart phones and tablets, while ensuring its appropriate use with respect to age and grade level of the learners, are likewise
encouraged.
The value of Mathematics as a learning area should not be confined in the corners of a classroom or any learning space. Its application to
real-life world problems should be dealt with depth and breadth which may be mirrored in classroom instruction.
Teachers, as the instructional leader in the implementation of the curriculum in the classroom, should use the identified most essential
learning competencies as outlined in this document to help them decide on how to scaffold the achievement of the learning goals and
meaningful learning in Math, in a reduced time allotment.

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Examples:
Grade 1: Quarter 1
Learning Competencies Comments/Recommendation Identified MELCs
Visualizes and represents numbers from 0 to 100 using a
variety of materials
Clustered as counting the
number of objects subsumed or
is part of visualizing and
representing numbers
Visualizes and represents numbers from 0 to 100 using a
variety of materials and methods
Counts the number of objects in a given set by ones and tens
Visualizes and count by 2s, 5s, and 10s through 100
Composes and decomposes a given number, e.g. 5 is 5 and 0,
4 and 1, 3 and 2, 2 and 3, 1 and 4 and 0 and 5
Omitted as this will is also
discussed in Quarter 3
Visualizes, represents and compares two sets using
expressions “less than,” “more than,” and “as many as”
Clustered and rephrased Compares two sets using the expressions “less than,” “more
than,” and “as many as” and orders sets from least to greatest
and vice versa
Visualizes, represents and orders sets from least to greatest
and vice versa
Visualizes, represents and compares numbers up to 100 using
relation symbols
Clustered and rephrased Compares numbers up to 100 using relations symbols and
ordering them in increasing and decreasing order
Visualizes, represents and orders numbers up to 100 in
increasing or decreasing order
Identifies the 1st
, 2nd
, 3rd
up to 10th
object in a given set from
a given point of reference
Clustered and rephrased Identifies, reads and writes ordinal numbers: 1st
, 2nd
, 3rd
, up
to 10th
object in a given set from a given point of reference
Reads and writes ordinal numbers: 1st
, 2nd
, 3rd
up to 10th
Grade 2, Quarter 4
Visualizes and finds the elapsed time in days Omitted, subsumed in the next LC Visualizes, represents and solves problems involving time
(minutes including a.m. and p.m. and elapsed time in days)
Shows and uses the appropriate unit of length and their
abbreviation cm and m to measure a particular object
Clustered and rephrased Measures objects using appropriate measuring tools and
units of length in m or cm
Measures objects using appropriate measuring tools in m or
cm
Compares length in meters or centimeters Clustered and rephrased; the
mathematical focus is on the
comparing measures
Compares the following unit of measures:
a. Length in meters or centimeters
b. Mass in grams or kilograms
c. Capacity in mL or L
Compares mass in grams or kilograms

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Shows and uses the appropriate unit of weight and their
abbreviations g and kg to measure a particular object
Clustered and rephrased Measures objects using appropriate measuring tools and
measuring units in g or kg
Measures objects using appropriate measuring units in g or
kg
Illustrates area as measure of how much surface is covered
or occupied by a plane figure
Omitted, subsumed in the LC of finding the area
using square tiles
Collects data on one variable using questionnaire Omitted, learners have better grasps of this LC
in Grade 4 be as they may not be somehow
struggling in reading and writing
Sorts, classifies, and organizes data in tabular form and
present this into a pictograph without and with scales
Tells whether an event is likely, equally likely, unlikely to
happen
Omitted as this may also be taken in Grade 3
for the discussion of probability of events
Describe events in real-life situations using the phrases
“likely to happen” or “unlikely to happen” or “equally likely
to happen”
Grade 6 Quarter 2
Sets up proportions for groups of objects or numbers and for
given situation
omitted
Identifies real-life situations that make use of integers Clustered and rephrased Describe the set of integers and identify real-life
situations that make use of it
Describes the set of integers
Represents integers on the number line LC is subsumed to the next LC Compares and arranges integers on the number
line
Compares and arranges integers
Grade 8 Quarter 2
Learning Competency Comments/Recommendations Identified MELCS
Illustrates linear inequalities in two variables Clustered, rephrased Illustrates and graphs linear inequalities in two
variables
Graphs linear inequalities in two variables
Illustrates a linear function Clustered and rephrased Graphs and illustrates a linear function and its
(a) domain; (b) range; (c) table of values; (d)
intercepts; and (e) slope
Graphs a linear function and its (a) domain; (b) range; (c)
table of values; (d) intercepts; and (e) slope

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How to Use the MELCs in Math
1. Appraise the content standards in each quarter of your grade level. This will guide you on tracking the
learning content being focused per quarter.
2. Plan the instructional activities suited for the type of learning delivery modality being used based from the
performance standards specified in that particular quarter. Ensure the appropriateness of the learning
materials, instructional resources and/or instructional device to be utilized to achieve these standards.
3. Examine the identified most essential competencies for each quarter. This will be the learning goal for the
quarter. Break it down to each month, then per week, then per day. If the learning competency is seemingly
a big chunk of a learning goal, then it has to be sub-tasked. But bear in mind that the development of the
math skill is arguably of more importance than the competence of content-knowledge in Math. For example,
place a great emphasis on how to perform operations on fractions and how it can be utilized in real life
context than on defining the different types of fractions
4. In your instructional/learning plans, design activities or assessment tasks where learners will have a great
deal of analysis and problem-solving. A case in point is on analyzing the graph of an equation where tasks
should not be concentrated on how the learners will draw the graph of the equation as this may be
augmented through the use of spreadsheets or software application, but on the analysis of the graph and
how these graph is illustrated to solve real-life problems.

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Department of Education
Bureau of Curriculum Development
Curriculum Standards Development Division
Meralco Avenue, Pasig City
Grade 1 to 10
MATHEMATICS
Most Essential Learning Competencies
School Year 2020-2021

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Grade Level: Grade 1
Subject: Mathematics
Quarter Content
Standards
The learner…
Performance
Standards
The learner…
Most Essential Learning competencies
The learner…
Duration K to 12 CG Code
Q1 demonstrates
understanding of
whole numbers
up to 100,
ordinal numbers
up to 10th,
money up to
PhP100.
1. is able to
recognize,
represent, and
order whole
numbers up to 100
and money up to
PhP100 in various
forms and contexts.
2. is able to
recognize, and
represent ordinal
numbers up to
10th, in various
forms and contexts.
Visualizes,represents and counts numbers
from 0 to 100 using a variety of materials and
methods.
Week 1 M1NS-Ia-1.1
identifies the number that is one more or one
less from a given number.
Week 2 M1NS-Ib-3
regroups sets of ones into sets of tens and sets
of tens into hundreds using objects.
Week 3 M1NS- Id-5
compares two sets using the expressions “less
than,” “more than,” and “as many as” and
orders sets from least to greatest and vice versa.
Week 4
reads and writes numbers up to 100 in symbols
and in words.
Week 5 M1NS-If-9.1
visualizes and gives the place value and value of
a digit in one- and two-digit numbers.
Week 6 M1NS-Ig-10.1
renames numbers into tens and ones. M1NS-Ig-11
compares numbers up to 100 using relation
symbol and orders them in increasing or
decresing order.
Week 7
Identifies, reads and writes ordinal numbers: 1st
, 2nd, 3rd, up to 10th object in a given set from
a given point of reference.
Week 8
recognizes and compares coins and bills up to
PhP100 and their notations.
Week 9 M1NS-Ij-19.1
Q2 illustrates addition as “putting together or
combining or joining sets”
Week 1 to 2
M1NS-IIa-23

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Quarter Content
Standards
The learner…
Performance
Standards
The learner…
The learner…
demonstrates
understanding of
addition and
subtraction of
whole numbers
up to 100
including money
is able to apply
addition and
subtraction of
whole numbers up
to 100 including
money in
mathematical
problems and real-
life situations.
visualizes and adds the following numbers using
appropriate techniques:
a. two one-digit numbers with sums up to 18
b. three one-digit numbers
c. numbers with sums through 99 without and
with regrouping
visualizes and solves one-step routine and non-
routine problems involving addition of whole
numbers including money with sums up to 99
using appropriate problem solving strategies.
Week 3
M1NS-IIe-29.1
illustrates subtraction as “taking away” or
“comparing” elements of sets.
Week 4
M1NS-IIf-24
illustrates that addition and subtraction are
inverse operations.
M1NS-IIf-25
visualizes, represents, and subtracts the
following numbers:
a. one-digit numbers with minuends through 18
(basic facts)
b. one- to two-digit numbers with minuends up
to 99 without regrouping
c. one- to two-digit numbers with minuends up
to 99 with regrouping
Week 5 to 6
subtracts mentally one-digit numbers from two-
digit minuends without regrouping using
appropriate strategies.
Week 7
M1NS-IIi-33.1
visualizes, represents, and solves routine and
non-routine problems involving subtraction of
whole numbers including money with minuends
Week 8
M1NS-IIi-34.1

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Quarter Content
Standards
The learner…
Performance
Standards
The learner…
The learner…
up to 99 with and without regrouping using
appropriate problem solving strategies and
tools.
Q3 demonstrates
understanding of
fractions ½ and
1/4.
is able to recognize,
represent, and
compare fractions
½ and 1/4 in
various forms and
contexts.
counts groups of equal quantity using concrete
objects up to 50 and writes an equivalent
expression. e.g. 2 groups of 5
Week 1
M1NS-IIIa-37
visualizes, represents, and separates objects
into groups of equal quantity using concrete
objects up to 50. e.g. 10 grouped by 5s
M1NS-IIIa-48
visualizes, represents, divides a whole into
halves and fourths and identifies ½ and ¼ of a
whole object.
Week 2
visualizes, represents and divides the elements
of sets into two groups of equal quantities to
show halves and four groups of equal
quantities to show fourths
Week 3
visualizes and draws the whole region or set
given its ½ and/or ¼
Week 4
M1NS-IIId-75
demonstrates
understanding of
2-dimensional
and 3-
dimensional
figures.
is able to describe,
compare, and
construct 2-
dimensional and 3-
dimensional objects
identifies, names, and describes the four basic
shapes (square, rectangle, triangle and circle)
in 2-dimensional (flat/plane) and 3-
dimensional (solid) objects.
Week 5
M1GE-IIIe-1
draws the four basic shapes. Week 6 M1GE-IIIf-3
constructs three dimensional objects (solid)
using manipulative materials.
M1GE-IIIf-4
demonstrates
understanding of
is able to apply
knowledge of
determines the missing term/s using one
attribute in a given continuous pattern
(letters/ numbers/events) and in a given
Week 7

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Quarter Content
Standards
The learner…
Performance
Standards
The learner…
The learner…
continuous and
repeating
patterns and
mathematical
sentences.
continuous and
repeating patterns
and number
sentences in
various situations.
repeating pattern (letters, numbers, colors,
figures, sizes, etc.).
constructs equivalent number expression
using addition and subtraction.
e.g. 6 + 5 = 12 - 1
Week 8
M1AL-IIIh-8
identifies and creates patterns to compose and
decompose using addition.
e.g. 7 = 0 + 7, 1 + 6, 2 + 5, 3 + 4, 4 + 3, 5 + 2, 6
+ 1, 7 + 0
M1AL-IIIi-9
visualizes and finds the missing number in an
addition or subtraction sentence using a
variety of ways
e.g. n + 2 = 5 5 – n = 3
Week 9
M1AL-IIIj-10
Q4 demonstrates
understanding of
time and non-
standard units of
length, mass and
capacity.
is able to apply
knowledge of time
and non-standard
measures of length,
mass, and capacity
in mathematical
problems and real-
life situations
tells the days in a week; months in a year in the
right order.
Week 1
M1ME-IVa-1
determines the day or the month using a
calendar.
Week 2
M1ME-IVa-2
tells and writes time by hour, half-hour and
quarter-hour using analog clock.
Week 3
M1ME-IVb-3
solves problems involving time (days in a week,
months in a year, hour, half-hour, and quarter-
hour)
Week 4
M1ME-IVb-4
compares objects using comparative words:
short, shorter, shortest; long, longer, longest;
heavy, heavier, heaviest; light, lighter, lightest.
Week 5 to 6
M1ME-IVc-19
estimates and measures length, mass and
capacity using non- standard units of
measures.
Week 7

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Quarter Content
Standards
The learner…
Performance
Standards
The learner…
The learner…
demonstrates
understanding of
pictographs
without scales
and outcomes of
an event.
is able to interpret
simple
representations of
data (tables and
pictographs
without scales).
infers and interprets data presented in a
pictograph without scales.
e.g. finding out from the title what the
pictograph is all about, comparing which has
the least or greatest …
Week 8
M1SP-IVh-3.1
solves routine and non-routine problems using
data presented in pictograph without scales.
Week 9 M1SP-IVh-4.1
Quarter Content Standards
The learner…
Performance
Standards
The learner…
The learner…
Q1
1. demonstrates
understanding of
whole numbers up
to 1000, ordinal
numbers up to
20th, and money
up to PhP100.
2. demonstrates
understanding of
1. is able to
recognize,
represent,
compare, and
order whole
numbers up to
1000, ordinal
numbers up to
20th, and money
up to PhP100 in
visualizes and represents numbers from 0-1000
with emphasis on numbers 101 – 1 000 using a
variety of materials.
Week 1
M2NS-Ia-1.2
gives the place value and finds the value of a digit
in three-digit numbers.
M2NS-Ib-10.2
visualizes and counts numbers by 10s, 50s, and
100s.
Week 2
M2NS-Ib-8.2
reads and writes numbers up to 1 000 in symbols
and in words.
M2NS-Ic-9.2
visualizes and writes three-digit numbers in
expanded form.
Week 3
M2NS-Ic-14
compares numbers up using relation symbols and
orders numbers up to 1 000 in increasing or
decreasing order.

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The learner…
Performance
Standards
The learner…
The learner…
addition of whole
numbers up to
1000 including
money.
various forms and
contexts.
2. is able to
recognize and
represent ordinal
numbers up to
20th in various
forms and
contexts.
3. is able to apply
addition of whole
numbers up to
1000 including
money in
mathematical
problems and
real-life
situations.
Identifies, reads and writes ordinal numbers from
1st through the 20th object in a given set from a
given point of reference.
Week 4
reads and writes money in symbols and in words
through PhP100.
M2NS-If-20.1
counts the value of a set of bills or a set of coins
through PhP100 (peso-coins only; centavo-coins
only; peso-bills only and combined peso-coins and
peso-bills).
Week 5
M2NS-If-21
compares values of different denominations of
coins and paper bills through PhP100 using
relation symbols.
M2NS-If-22.1
illustrates the properties of addition
(commutative, associative, identity) and applies
each in appropriate and relevant situations.
Week 6
M2NS-Ig-26.3
visualizes, represents, and adds the following
numbers with sums up to 1000 without and with
regrouping:
a. 2-digit by 3-digit numbers
b. 3-digit by 3-digit numbers
adds mentally the folllowing numbers using
appropriate strategies:
a. 1- to 2-digit numbers with sums up to 50
b. 3-digit numbers and 1-digit numbers
c. three -digit numbers and tens (multiples of 10
up to 90)
d. 3-digit numbers and hundreds (multiples of 100
up to 900)
Week 7 to 8

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The learner…
Performance
Standards
The learner…
The learner…
solves routine and non-routine problems involving
addition of whole numbers including money with
sums up to 1000 using appropriate problem
solving strategies and tools.
Week 9
M2NS-Ij-29.2
Q2 demonstrates
understanding of
subtraction and
multiplication of
whole numbers up
to 1000 including
money.
is able to apply
subtraction and
multiplication of
whole numbers
up to 1000
including money
in mathematical
problems and
real-life
situations.
visualizes, represents, and subtracts 2- to 3-digit
numbers with minuends up to 999 without and
with regrouping.
Week 1
M2NS-IIa-32.5
subtracts mentally the following numbers without
regrouping using appropriate strategies:
a. 1-digit numbers from 1- to 3-digit numbers
b. 3-digit numbers by tens and by hundreds
Week 2
subtraction of whole numbers including money
with minuends up to 1000 using appropriate
problem solving strategies and tools.
Week 3
M2NS-IIc-34.2
performs orders of operations involving addition
and subtractions of small numbers.
Week 4
M2NS-IId-34.3
solves multi-step routine and non-routine
problems involving addition and subtraction of 2-
to 3-digit numbers including money using
appropriate problem solving strategies and tools.
Week 5
M2NS-IIe-34.4
illustrates and writes a related equation for each
type of multiplication: repeated addition, array,
counting by multiples, and equal jumps on the
number line.
Week 6
illustrates the following properties of
multiplication and applyc each in relevant
situation: (a) identity, (b) zero, and, (c)
commutative.
Week 7

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The learner…
Performance
Standards
The learner…
The learner…
visualizes multiplication of numbers 1 to 10 by
2,3,4,5 and10.
Week 8
M2NS-IIh-41.1
multiplies mentally 2,3,4,5 and 10 using
appropriate strategies.
M2NS-IIi-42.1
appropriate problem solving strategies and tools:
a. multiplication of whole numbers including
money
b. multiplication and addition or subtraction of
whole numbers including money
Week 9
Q3
1. demonstrates
understanding of
division of whole
numbers up to
1000 including
money.
2. demonstrates
understanding of
unit fractions.
1. is able to apply
division of whole
numbers up to
1000 including
money in
mathematical
problems and
real-life
situations.
2. is able to
recognize and
represent unit
fractions in
various forms and
contexts.
visualizes and represents division, and writes a
related equation for each type of situation: equal
sharing, repeated subtraction, equal jumps on the
number line, and formation of equal groups of
objects.
Week 1
visualizes division of numbers up to 100 by 2,3,4,5,
and 10 (multiplication table of 2, 3, 4, 5 and 10).
Week 2
M2NS-IIIb-51.1
divides mentally numbers by 2,3,4,5 and 10 using
appropriate strategies (multiplication table of 2, 3,
4, 5 and 10).
Week 3
M2NS-IIIb-52.1
illustrates that multiplication and division are
inverse operations.
M2NS-IIIc-53
division of numbers by 2,3,4,5 and 10 and with
any of the other operations of whole numbers
including money using appropriate problem
Week 4
M2NS-IIIc-56.1
visualizes,representsandidentifiesunitfractionswith
denominatorsof10andbelow.
Week 5 to 6
M2NS-IIId-72.2

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The learner…
Performance
Standards
The learner…
The learner…
reads and writes unit fractions. M2NS-IIId-76.1
compares using relation symbol and arranges in
increasing or decreasing order the unit fractions.
identifies other fractions less than one with
denominators 10 and below.
M2NS-IIIe-79.1
visualizes(usinggroupofobjectsandnumberline),reads
andwritessimilarfractions
compares similar fractions using relation symbols. Week 7 M2NS-IIIf-77.2
arranges similar fractions in increasing or
decreasing order.
M2NS-IIIf-78.2
demonstrates
understanding of
straight and curved
lines, flat and
curved surfaces
and basic shapes.
is able to
recognize and
construct straight
and curved lines,
flat and curved
surfaces and basic
shapes
constructs squares, rectangles, triangles, circles,
half-circles, and quarter circles using cut-outs and
square grids.
Week 8
M2GE-IIIg-6
identifies straight lines and curves, flat and curved
surfaces in a 3-dimensional object.
M2GE-IIIi-9
demonstrates
understanding of
continuous
patterns using two
attributes
is able to apply
knowledge of
continuous
patterns using
two attributes
determines the missing term/s in a given
continuous pattern using two attributes (any
two of the following: figures, numbers,
colors, sizes, and orientations, etc.) e.g. 1,
A, 2,B,3,C,__,__
Week 9
M2AL-IIIj-3
Q4 demonstrates
understanding
of time,
standard
measures of
length, mass
is able to apply
knowledge of
time, standard
measures of
length, weight,
and capacity, and
tells and writes time in minutes including
a.m. and p.m. using analog and digital clocks.
Week 1
M2ME-IVa-5
visualizes, represents, and solves problems
involving time (minutes including a.m. and
p.m. and elapsed time in days).
compares the following unit of measures: Week 2

16
The learner…
Performance
Standards
The learner…
The learner…
and capacity
and area
using square-
tile units.
area using square-
tile units in
mathematical
problems and
real-life
situations.
a. length in meters or centimeters
b. mass in grams or kilograms
c. capacity in mL or L
measures objects using appropriate
measuring tools and unit of leangth in m or
cm.
Week 3
estimates and measures length using meter
or centimeter.
M2ME-IVc-26
solves routine and non-routine problems
involving length.
Week 4
M2ME-IVc-27
measuring tools and measuring units in g or
kg.
Week 5
estimates and measures mass using gram or
kilogram.
M2ME-IVe-31
involving mass.
Week 6
M2ME-IVe-32
measuring tools in mL or L.
M2ME-IVf-33
finds the area of a given figure using square-
tile units i.e. number of square-tiles needed.
Week 7
M2ME-IVg-36
estimates the area of a given figure using
any shape.
M2ME-IVh-37
involving any figure using square tiles.
Week 8
M2ME-IVh-38
deepens
understanding of
is able to
interpret simple
infers and interprets data presented in a
pictograph without and with scales.
Week 9
M2SP-IVi-3.2

17
The learner…
Performance
Standards
The learner…
The learner…
pictographs
without and with
scales
representations
of data
(pictographs
without and with
scales)
using data presented in a pictograph without
and with scales.
M2SP-IVi-4.2
The learner…
Performance
Standards
The learner…
The learner…
Q1
1. demonstrates
understanding of
whole numbers up
to 10 000, ordinal
numbers up to
100th, and money
up to PhP1000.
2. demonstrates
understanding of
addition and
subtraction of
1. is able to
recognize,
represent,
compare, and
order whole
numbers up to 10
000, and money
up to PhP1000 in
various forms
and contexts.
visualizes numbers up to 10 000 with emphasis on
numbers 1001 - 10000.
Week 1
M3NS-Ia-1.3
gives the place value and value of a digit in 4- to 5-
digit numbers.
M3NS-Ia-10.3
reads and writes numbers up to 10 000 in symbols
and in words.
M3NS-Ia-9.3
rounds numbers to the nearest ten, hundred and
thousand..
Week 2
M3NS-Ib-15.1
compares using relation symbols and orders in
increasing or decreasing order 4- to 5-digit
numbers up to 10 000.
identifies ordinal numbers from 1st to 100th with
emphasis on the 21st to 100th object in a given set
from a given point of reference.
Week 3
M3NS-Ic-16.3
recognizes, reads and writes money in symbols and
in words through PhP1 000 in pesos and centavos

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The learner…
Performance
Standards
The learner…
The learner…
whole numbers
including money
2. is able to
recognize and
represent,
ordinal numbers
up to 100th in
various forms
and contexts.
3. is able to apply
addition and
subtraction of
whole numbers
including money
in mathematical
problems and
real-life
situations.
compares values of the different denominations of
coins and bills through PhP1 000 using relation
symbols.
Week 4
M3NS-Id-22.2
adds 3- to 4-digit numbers up to three addends
with sums up to 10 000 without and with
regrouping.
M3NS-Id-27.6
estimates the sum of 3- to 4-digit addends with
reasonable results.
Week 5
M3NS-Ie-31
adds mentally the following numbers using
a. 2-digit and 1-digit numbers without or with
regrouping
b. 2- to 3-digit numbers with multiples of
hundreds
addition of whole numbers with sums up to 10 000
including money using appropriate problem solving
strategies and tools.
Week 6
M3NS-If-29.3
subtracts 3-to 4-digit numbers from 3- to 4-digit
numbers without and with regrouping.
Week 7
M3NS-Ig-32.6
estimates the difference of two numbers with
three to four digits with reasonable results.
M3NS-Ih-36
subtracts mentally the following numbers using
a. 1- to 2-digit numbers without and with
regrouping
b. 2-to3-digitnumberswithmultiplesofhundreds
withoutandwithregrouping
Week 8

19
The learner…
Performance
Standards
The learner…
The learner…
subtraction without or with addition of whole
numbers including money using appropriate
Week 9
M3NS-Ii-34.5
Q2 demonstrates
understanding of
multiplication and
division of whole
numbers including
money.
is able to apply
multiplication
and division of
whole numbers
including money
in mathematical
problems and
real-life
situations
visualizes multiplication of numbers 1 to 10 by
6,7,8 and 9.
Week 1
M3NS-IIa-41.2
visualizes and states basic multiplication facts for
numbers up to 10.
M3NS-IIa-41.3
Illustrates the properties of multiplication in
relevant situations (commutative property,
distributive property or associative property)
Week 2 to 3
multiplies numbers:
a. 2- to 3-digit numbers by 1-digit numbers
without or with regrouping
b. 2-digit numbers by 2-digit numbers without
regrouping
c. 2-digit number by 2-digit numbers with
regrouping
d. 2- to 3-digit numbers by multiples of 10 and
100
e. 1- to 2-digit numbers by 1 000
estimates the product of 2- to 3-digit numbers and
1- to 2-digit numbers with reasonable results .
Week 4
M3NS-IId-44.1
multiplies mentally 2-digit by 1-digit numbers
without regrouping with products of up to 100.
M3NS-IIe-42.2
multiplication without or with addition and
subtraction of whole numbers including money
Week 5
M3NS-IIe-45.3

20
The learner…
Performance
Standards
The learner…
The learner…
using appropriate problem solving strategies and
tools.
visualizes and states the multiples of 1- to 2-digit
numbers.
Week 6
M3NS-IIf-47
visualizes division of numbers up to 100 by
6,7,8,and 9 (multiplication table of 6, 7, 8, and 9).
M3NS-IIg-51.2
visualizes and states basic division facts of numbers
up to 10.
Week 7
M3NS-IIg-51.3
divides numbers without or with remainder:
a. 2- to 3-digit numbers by 1- to 2- digit
numbers
b. 2-3 digit numbers by 10 and 100
estimates the quotient of 2- to 3- digit numbers by
1- to 2- digit numbers.
Week 8
M3NS-IIi-55.1
divides mentally 2-digit numbers by 1-digit
numbers without remainder using appropriate
strategies.
M3NS-IIi-52.2
division of 2- to 4-digit numbers by 1- to 2-digit
numbers without or with any of the other
operations of whole numbers including money
using appropriate problem solving strategies and
tools.
Week 9
M3NS-IIj-56.2
Q3 demonstrates
understanding of
proper and
improper, similar
and dissimilar and
is able to
recognize and
represent proper
and improper,
similar and
dissimilar and
identifies odd and even numbers. Week 1 M3NS-IIIa-63
visualizes and represents fractions that are equal
to one and greater than one using regions, sets and
number line.
reads and writes fractions that are equal to one
and greater than one in symbols and in words.
Week 2
M3NS-IIIb-76.3

21
The learner…
Performance
Standards
The learner…
The learner…
equivalent
fractions.
equivalent
fractions in
various forms
and contexts.
Represents, compares and arranges dissimilar
fractions in increasing or decreasing order.
Week 3
visualizes and generates equivalent fractions.
Week 4
M3NS-IIIe-72.7
demonstrates
understanding of
lines and
symmetrical
designs
is able to
recognize and
represent lines in
real objects and
designs or
drawings and
complete
symmetrical
designs
recognizes and draws a point, line, line segment
and ray.
Week 5
M3GE-IIIe-11
recognizes and draws parallel, intersecting and
perpendicular lines.
M3GE-IIIf-12.1
visualizes, identifies and draws congruent line
segments.
Week 6
M3GE-IIIf-13
identifies and visualizes symmetry in the
environment and in design.
M3GE-IIIg-7.3
identifies and draws the line of symmetry in a given
symmetrical figure.
Week 7
M3GE-IIIg-7.4
completes a symmetric figure with respect to a
given line of symmetry.
M3GE-IIIh-7.5
demonstrates
understanding of
continuous and
repeating patterns
and mathematical
sentences
involving
multiplication and
division of whole
numbers.
is able to apply
knowledge of
continuous and
repeating
patterns and
number
sentences
involving
multiplication or
division of whole
numbers in
determines the missing term/s in a given
combination of continuous and repeating pattern.
e.g. 4A,5B, 6A,7B,__
1 2 3 4 ___
Week 8
M3AL-IIIi-4
finds the missing value in a number sentence
involving multiplication or division of whole
numbers.
e.g. n x 7 = 56 56 ÷ n = 8
Week 9
M3AL-IIIj-12

22
The learner…
Performance
Standards
The learner…
The learner…
various
situations.
Q4 demonstrates
understanding of
conversion of
time, linear, mass
and capacity
measures and area
of square and
rectangle.
is able to apply
knowledge of
conversion of
time, linear, mass
and capacity
measures and
area of rectangle
and square in
mathematical
problems and
real-life
situations.
visualizes, represents, and converts time
measure:
a. from seconds to minutes, minutes to hours,
and hours to a day and vice versa
b. days to week, month and year and vice versa
c. weeks to months and year and vice versa
d. months to year and vice versa.
Week 1
solves problems involving conversion of time
measure.
Week 2
visualizes, and represents, and converts common
units of measure from larger to smaller unit and
vice versa: meter and centimeter, kilogram and
gram, liter and milliliter.
Week 3
M3ME-IVb-39
visualizes, and represents, and solves routine and
non-routine problems involving conversions of
common units of measure.
M3ME-IVc-40
involving capacity measure.
Week 4
visualizes, and represents, and measures area
using appropriate unit.
Week 5
M3ME-IVd-43
involving areas of squares and rectangles.
M3ME-IVf-46
demonstrates
understanding of
bar graphs and
outcomes of an
is able to create
and interpret
simple
representations
collects data on one variable using existing
records.
Week 6
M3SP-IVg-1.3
sorts, classifies, and organizes data in tabular
form and presents this into a vertical or
horizontal bar graph.
M3SP-IVg-2.3

23
The learner…
Performance
Standards
The learner…
The learner…
event using the
terms sure, likely,
equally likely,
unlikely, and
impossible to
happen.
of data (tables
and single bar
graphs) and
describe
outcomes of
familiar events
using the terms
sure, likely,
equally likely,
unlikely, and
impossible to
happen.
infers and interprets data presented in different
kinds of bar graphs (vertical/ horizontal).
Week 7
M3SP-IVh-3.3
data presented in a single-bar graph.
Week 8
M3SP-IVh-4.3
tells whether an event is sure, likely, equally
likely, unlikely, and impossible to happen.
Week 9
M3SP-IVi-7.3
describes events in real-life situations using the
phrases “sure to happen,“ likely to happen”,
“equally likely to happen”, “unlikely to happen”,
and “impossible to happen”.
M3SP-IVj-8.3

24
The learner…
Performance
Standards
The learner…
The learner…
Q1
1. demonstrates
understanding of
whole numbers up
to 100,000.
2. demonstrates
understanding of
multiplication and
division of whole
numbers including
money.
1. is able to recognize
and represent whole
numbers up to
100,000 in various
forms and contexts.
2. is able to apply
multiplication and
division of whole
numbers including
money in
mathematical
problems and real-life
situations.
visualizes numbers up to 100 000 with
emphasis on numbers 10 001–100 000.
Week 1
M4NS-Ia-1.4
gives the place value and value of a digit in
numbers up to 100 000.
M4NS-Ia-10.4
reads and writes numbers, in symbols and
in words, up to hundred thousand and
compare them using relation symbols
rounds numbers to the nearest thousand
and ten thousand.
Week 2
M4NS-Ib-5.2
orders numbers up to 100 000 in increasing
or decreasing order.
M4NS-Ib-13.4
multiplies numbers up to 3-digit numbers
by up to 2-digit numbers without or with
regrouping.
Week 3
M4NS-Ic-43.7
estimates the products of 3- to 4-digit
numbers by 2- to 3- digit numbers with
reasonable results.
M4NS-Ic-44.2
multiplies mentally 2-digit by 1-to 2-digit
numbers with products up to 200 and
explains the strategies used.
Week 4
M4NS-Id-42.3
involving multiplication of whole numbers
including money using appropriate
M4NS-Id-45.4
problems involving multiplication and
Week 5
M4NS-Ie-45.5

25
The learner…
Performance
Standards
The learner…
The learner…
addition or subtraction using appropriate
divides 3- to 4-digit numbers by 1-to 2-digit
numbers without and with remainder.
Week 6
M4NS-If-54.3
divides mentally 2- to 4-digit numbers by
tens or hundreds or by 1 000 without and
with remainder.
estimates the quotient of 3- to 4-digit
dividends by 1- to 2-digit divisors with
reasonable results.
Week 7
M4NS-Ig-55.2
involving division of 3- to 4-digit numbers
by 1- to 2-digit numbers including money
using appropriate problem solving
Week 8
M4NS-Ih-56.3
problems involving division and any of the
other operations of whole numbers
including money using appropriate problem
M4NS-Ih-56.4
performs a series of two or more
operations applying Multiplication, Division,
Addition, Subtraction (MDAS) correctly.
Week 9
Q2
1. demonstrates
understanding of
factors and
multiples and
1. is able to apply
knowledge of factors
and multiples, and
addition and
identifies factors of a given number up to
100.
Week 1
M4NS-IIa-64
identifies the multiples of a given number
up to 100.
M4NS-IIa-65
differentiates prime from composite
numbers.
M4NS-IIb-66

26
The learner…
Performance
Standards
The learner…
The learner…
addition and
subtraction of
fractions.
2. demonstrates
understanding of
improper fractions,
mixed numbers
and decimals
subtraction of
fractions in
mathematical
situations.
and represent
improper fractions,
mixed numbers and
decimals
writes a given number as a product of its
prime factors.
Week 2 M4NS-IIb-67
finds the common factors, greatest
common factor (GCF), common multiples
and least common multiple (LCM) of two
numbers using the following methods:
listing, prime factorization, and continuous
division.
solves real-life problems involving GCF and
LCM of 2 given numbers.
Week 3 M4NS-IId-70.1
changes improper fraction to mixed
numbers and vice versa.
Week 4
M4NS-IIe-80
changes fractions to lowest forms. M4NS-IIe-81
visualizes addition and subtraction of
similar and dissimilar fractions.
Week 5
visualizes subtraction of a fraction from a
whole number.
M4NS-IIf-82.2
performs addition and subtraction of
similar and dissimilar fractions.
Week 6
M4NS-IIg-83
involving addition and/or subtraction of
fractions using appropriate problem solving
M4NS-IIh-87.1
visualizes decimal numbers using models
like blocks, grids, number lines and money
to show the relationship to fractions.
Week 7
M4NS-IIi-99
renames decimal numbers to fractions,
and fractions whose denominators are
factors of 10 and 100 to decimals.
M4NS-IIi-100

27
The learner…
Performance
Standards
The learner…
The learner…
gives the place value and the value of a
digit of a given decimal number through
hundredths.
Week 8
M4NS-IIi-101.1
reads and writes decimal numbers through
hundredths.
M4NS-IIj-102.1
rounds decimal numbers to the nearest
whole number and tenth.
Week 9
M4NS-IIj-103.1
compares and arranges decimal numbers. M4NS-IIj-104.1
Q3 demonstrates
understanding of
the concepts of
parallel and
perpendicular
lines, angles,
triangles, and
quadrilaterals.
is able to describe
parallel and
perpendicular lines,
angles, triangles, and
quadrilaterals
describes and draws parallel, intersecting,
and perpendicular lines using ruler and set
square.
Week 1
describes and illustrates different angles
(right, acute, and obtuse) using models.
Week 2
M4GE-IIIb-14
describes the attributes/properties of
triangles and quadrilaterals using concrete
objects or models.
M4GE-IIIb-15
identifies and describes triangles according
to sides and angles.
Week 3
M4GE-IIIc-16
identifies and describes the different kinds
of quadrilaterals: square, rectangle,
parallelogram, trapezoid, and rhombus.
M4GE-IIIc-17
relates triangles to quadrilaterals
Week 4 M4GE-IIId-18.1
relates one quadrilateral to another
quadrilateral (e.g. square to rhombus).
M4GE-IIId-18.2
demonstrates
understanding of
concepts of
continuous and
is able to identify the
missing element in a
pattern and number
sentence.
determines the missing term/s in a
sequence of numbers (e.g. odd numbers,
even numbers, multiples of a number,
factors of a number, etc.)
Week 5
M4AL-IIIe-5

28
The learner…
Performance
Standards
The learner…
The learner…
repeating patterns
and number
sentences.
e.g. 3,6,9,__ 4,8,12,16,__ (e.g.
odd numbers, even numbers, multiples of
a number, factors of a number, etc.)
1 2 3 4 5 6 7 ____
finds the missing number in an equation
involving properties of operations. (e.g.
(4+__ ) + 8 = 4 + ( 5 + __)
M4AL-IIIe-13
demonstrates
understanding of
the concept of
time, perimeter,
area, and volume.
is able to apply the
concepts of time,
perimeter, area, and
volume to
mathematical
situations.
finds the elapsed time in minutes and
seconds.
Week 6
M4ME-IIIf-11
estimates the duration of time in minutes. M4ME-IIIf-12
solves problems involving elapsed time. M4ME-IIIg-13
visualizes the perimeter of any given plane
figure in different situations.
Week 7
M4ME-IIIg-48
measures the perimeter of any given figure
using appropriate tools.
M4ME-IIIh-49
finds the perimeter of triangles, squares,
rectangles, parallelograms, and trapezoids.
M4ME-IIIi-51
in real-life situations involving perimeter
of squares and rectangles, triangles,
parallelograms, and trapezoids.
Week 8
M4ME-IIIi-52
differentiates perimeter from area. Week 9 M4ME-IIIj-53
converts sq. cm to sq. m and vice versa. M4ME-IIIj-54
Q4 finds the area of irregular figures made up
of squares and rectangles using sq. cm and
sq. m.
Week 1
M4ME-IVa-55
finds the area of triangles, parallelograms
and trapezoids using sq. cm and sq. m.
M4ME-IVb-58

29
The learner…
Performance
Standards
The learner…
The learner…
involving squares, rectangles, triangles,
parallelograms, and trapezoids.
Week 2
M4ME-IVc-60
visualizes the volume of solid figures in
different situations using non-standard (e.g.
marbles, etc.) and standard units.
Week 3
M4ME-IVd-62
finds the volume of a rectangular prism
using cu. cm and cu. m.
M4ME-IVe-64
involving the volume of a rectangular prism.
Week 4
M4ME-IVf-65
demonstrates
understanding of
the concepts of
bar graphs and
simple
experiments.
is able to create and
interpret simple
representations of
data (tables and bar
graphs) and describe
outcomes in simple
experiments.
collects data on two variables using any
source.
Week 5
M4SP-IVg-1.4
organizes data in tabular form and presents
them in a single/double horizontal or
vertical bar graph.
M4SP-IVg-2.4
interprets data presented in different kinds
of bar graphs (vertical/horizontal,
single/double bars).
Week 6
M4SP-IVg-3.4
using data presented in a single or double-
bar graph.
M4SP-IVh-4.4
draws inferences based on data presented
in a double-bar graph.
Week 7
M4SP-IVh-5.4
records favorable outcomes in a simple
experiment (e.g. tossing a coin, spinning a
wheel, etc.)
M4SP-IVi-9
expresses the outcome in a simple
experiment in words, symbols, tables, or
graphs.
Week 8
M4SP-IVi-10

30
The learner…
Performance
Standards
The learner…
The learner…
explains the outcomes in an experiment. M4SP-IVi-11
involving a simple experiment.
Week 9
M4SP-IVj-12
The learner…
Performance
Standards
The learner…
The learner…
Duration
K to 12 CG Code
Q1
demonstrates
understanding of
divisibility, order of
operations, factors
and multiples, and
the four
fundamental
operations
involving fractions
is able to apply
divisibility, order of
operations, factors
and multiples, and the
four fundamental
operations involving
fractions in
mathematical
situations.
uses divisibility rules for 2, 5, and 10 to
find the common factors of numbers.
Week 1
M5NS-Ib-58.1
uses divisibility rules for 3, 6, and 9 to find
common factors.
M5NS-Ib-58.2
uses divisibility rules for 4, 8, 12, and 11
to find common factors.
Week 2
M5NS-Ib-58.3
involving factors, multiples, and divisibility
rules for 2,3,4,5,6,8,9,10,11, and 12.
M5NS-Ic-59
Performs a series of more than two
operations on whole numbers applying
Parenthesis, Multiplication, Division,
Addition, Subtraction (PMDAS) or
Grouping, Multiplication, Division,
Addition, Subtraction (GMDAS) correctly.
Week 3
finds the common factors, GCF, common
multiples and LCM of 2–4 numbers using
continuous division.
Week 4

31
The learner…
Performance
Standards
The learner…
The learner…
Duration
K to 12 CG Code
solves real-life problems involving GCF and
LCM of 2-3 given numbers.
M5NS-Ie-70.2
adds and subtracts fractions and mixed
fractions without and with regrouping.
Week 5
M5NS-Ie-84
fractions using appropriate problem
M5NS-If-87.2
visualizes multiplication of fractions using
models.
Week 6
M5NS-Ig-89
multiplies a fraction and a whole number
and another fraction.
M5NS-Ig-90.1
multiplies mentally proper fractions with
denominators up to 10.
M5NS-Ig-91
solves routine or non-routine problems
involving multiplication without or with
addition or subtraction of fractions and
whole numbers using appropriate
Week 7
M5NS-Ih-92.1
shows that multiplying a fraction by its
reciprocal is equal to 1.
M5NS-Ih-94
visualizes division of fractions. Week 8 M5NS-Ii-95
divides simple fractions and whole
numbers by a fraction and vice versa
M5NS-Ii-96.1
involving division without or with any of
the other operations of fractions and
whole numbers using appropriate
problem solving strategies and tools .
Week 9
M5NS-Ij-97.1

32
The learner…
Performance
Standards
The learner…
The learner…
Duration
K to 12 CG Code
Q2
1. demonstrates
understanding of
decimals.
2. demonstrates
understanding of
the four
fundamental
operations
involving decimals
and ratio and
proportion.
and represent
decimals in various
forms and contexts.
2. is able to apply the
four fundamental
decimals and ratio and
proportion in
mathematical
situations.
gives the place value and the value of a
digit of a given decimal number through
ten thousandths.
Week 1
M5NS-IIa-101.2
reads and writes decimal numbers
through ten thousandths.
M5NS-IIa-102.2
rounds decimal numbers to the nearest
hundredth and thousandth.
M5NS-IIa-103.2
compares and arranges decimal numbers. Week 2 M5NS-IIb-104.2
adds and subtracts decimal numbers
through thousandths without and with
regrouping.
M5NS-IIb-106.1
involving addition and subtraction of
decimal numbers including money using
appropriate problem solving strategies
and tools.
Week 3
M5NS-IIc-108.1
multiplies decimals up to 2 decimal places
by 1- to 2-digit whole numbers.
Week 4
M5NS-IId-111.1
multiplies decimals with factors up to 2
decimal places.
M5NS-IId-111.2
estimates the products of decimal
numbers with reasonable results.
Week 5
M5NS-IIe-112
addition or subtraction of decimals and
whole numbers including money using
and tools.
M5NS-IIe-113.1

33
The learner…
Performance
Standards
The learner…
The learner…
Duration
K to 12 CG Code
divides decimals with up to 2 decimal
places.
Week 6
M5NS-IIf-116.1
divides whole numbers with quotients in
decimal form.
M5NS-IIf-116.2
the other operations of decimals and
whole numbers including money using
and tools.
Week 7
M5NS-IIg-120.1
visualizes the ratio of 2 given numbers. M5NS-IIh-122
identifies and writes equivalent ratios. Week 8 M5NS-IIi-124
expresses ratios in their simplest forms. M5NS-IIi-125
finds the missing term in a pair of
equivalent ratios.
Week 9
M5NS-IIi-126
defines and describes a proportion. M5NS-IIj-127
recognizes when two quantities are in
direct proportion.
M5NS-IIj-128
Q3 demonstrates
understanding of
percent.
is able to apply
percent in
mathematical
situations
visualizes percent and its relationship to
fractions, ratios, and decimal numbers
using models.
Week 1
M5NS-IIIa-136
defines percentage, rate or percent, and
base.
M5NS-IIIa-137
identifies the base, percentage, and rate
in a problem.
M5NS-IIIa-138
finds the percentage in a given problem. Week 2 M5NS-IIIb-139
involving percentage using appropriate
M5NS-IIIb-140

34
The learner…
Performance
Standards
The learner…
The learner…
Duration
K to 12 CG Code
demonstrates
understanding of
polygons, circles,
and solid figures.
is able to construct
and describe
polygons, circles, and
solid figures.
visualizes, names, describes and draws
polygons with 5 or more sides.
Week 3
M5GE-IIIc-19
describes and compares properties of
polygons (regular and irregular polygons).
M5GE-IIIc-20
visualizes congruent polygons. M5GE-IIId-22
identifies the terms related to a circle. Week 4 M5GE-IIId-23.2
draws circles with different radii using a
compass.
M5GE-IIIe-24
visualizes and describes solid figures. Week 5 M5GE-IIIe-25
makes models of different solid figures:
cube, prism, pyramid, cylinder, cone, and
sphere using plane figures.
M5GE-IIIe-26
demonstrates
understanding of
the concept of
sequence and
solving simple
equations.
1. is able to apply the
knowledge of
sequence in various
situations.
2. is able to use
different problem
solving strategies
formulates the rule in finding the next
term in a sequence.
e.g. 1, 3, 7,15, (15 x 2+1) Possible
answers: (x 2 + 1) (+2, +4, +8, +16)
Week 6
M5AL-IIIf-6
uses different strategies (looking for a
pattern, working backwards, etc.) to solve
for the unknown in simple equations
involving one or more operations on
whole numbers and fractions.
e.g. 3 x _ + 1 = 10 (the unknown is solved
by working backwards)
M5AL-IIIf-14
demonstrates
understanding of
time and
circumference.
is able to apply
knowledge of time
and circumference in
mathematical
measures time using a 12-hour and a 24-
hour clock.
Week 7
M5ME-IIIg-14
calculates time in the different world time
zones in relation to the Philippines.
M5ME-IIIg-15
solves problems involving time. M5ME-IIIg-16
visualizes circumference of a circle. Week 8 M5ME-IIIh-67

35
The learner…
Performance
Standards
The learner…
The learner…
Duration
K to 12 CG Code
situations.
measures circumference of a circle using
appropriate tools.
M5ME-IIIh-68
finds the circumference of a circle. M5ME-IIIi-70
involving circumference of a circle.
Week 9
M5ME-IIIj-71
Q4 demonstrates
understanding of
area, volume and
temperature.
is able to apply
knowledge of area,
volume and
temperature in
mathematical
situations.
finds the area of a given circle. Week 1 M5ME-IVa-74
involving the area of a circle.
M5ME-IVb-75
visualizes the volume of a cube and
rectangular prism.
Week 2
M5ME-IVc-77
names the appropriate unit of measure
used for measuring the volume of a cube
and a rectangle prism.
M5ME-IVc-78
converts cu. cm to cu. m and vice versa;
cu.cm to L and vice versa.
M5ME-IVd-80
finds the volume of a given cube and
rectangular prism using cu. cm and cu. m.
Week 3
M5ME-IVd-81
estimates and uses appropriate units of
measure for volume.
M5ME-IVd-82
involving volume of a cube and
rectangular prism in real-life situations
using appropriate strategies and tools.
Week 4
M5ME-IVe-83
reads and measures temperature using
thermometer (alcohol and/or digital) in
degree Celsius.
Week 5
M5ME-IVf-85
involving temperature in real-life
situations.
M5ME-IVf-87

36
The learner…
Performance
Standards
The learner…
The learner…
Duration
K to 12 CG Code
demonstrates
understanding of
line graphs and
experimental
probability.
interpret
representations of
data (tables and line
graphs) and apply
experimental
probability in
mathematical
situations.
organizes data in tabular form and
presents them in a line graph.
Week 6
M5SP-IVg-2.5
interprets data presented in different
kinds of line graphs (single to double-line
graph).
M5SP-IVh-3.5
using data presented in a line graph.
Week 7
M5SP-IVh-4.5
draws inferences based on data presented
in a line graph.
M5SP-IVh-5.5
describes experimental probability. Week 8 M5SP-IVi-14
performs an experimental probability and
records result by listing.
M5SP-IVi-15
analyzes data obtained from chance using
experiments involving letter cards (A to Z)
and number cards (0 to 20).
Week 9
M5SP-IVi-16
involving experimental probability.
M5SP-IVj-17

37
The learner…
Performance
Standards
The learner…
The learner…
Q1 demonstrates
understanding of
the four
fundamental
operations
involving fractions
and decimals.
is able to apply the
four fundamental
fractions and decimals
in mathematical
situations.
adds and subtracts simple fractions and
mixed numbers without or with
regrouping.
Week 1
M6NS-Ia-86
M6NS-Ia-87.3
multiplies simple fractions and mixed
fractions.
Week 2
M6NS-Ib-90.2
addition or subtraction of fractions and
mixed fractions using appropriate problem
M6NS-Ib-92.2
divides simple fractions and mixed
fractions.
Week 3
M6NS-Ic-96.2
the other operations of fractions and mixed
M6NS-Ic-97.2
adds and subtracts decimals and mixed
decimals through ten thousandths without
or with regrouping.
Week 4
M6NS-Id-106.2
solves 1 or more steps routine and non-
routine problems involving addition and/or
M6NS-Id-108.2

38
The learner…
Performance
Standards
The learner…
The learner…
subtraction of decimals and mixed
decimals using appropriate problem solving
multiplies decimals and mixed decimals
with factors up to 2 decimal places.
Week 5
M6NS-Ie-111.3
multiplies mentally decimals up to 2
decimals places by 0.1, 0.01,10, and 100.
M6NS-Ie-111.4
involving multiplication of decimals and
mixed decimals including money using
appropriate problem solving strategies.
M6NS-Ie-113.2
solves multi-step problems involving
multiplication and addition or subtraction
of decimals, mixed decimals and whole
numbers including money using
appropriate problem solving strategies and
tools.
Week 6
M6NS-If-113.3
divides:
a. whole numbers by decimals up to 2
decimal places and vice versa
b. decimals/mixed decimals up to 2
decimal places
Week 7
divides decimals:
a. up to 4 decimal places by 0.1, 0.01,
and 0.001
b. up to 2 decimal places by 10, 100,
and 1 000 mentally
Week 8
differentiates terminating from repeating,
non-terminating decimal quotients.
Week 9
M6NS-Ii-119

39
The learner…
Performance
Standards
The learner…
The learner…
involving division of decimals, mixed
decimals, and whole numbers including
money using appropriate problem solving
M6NS-Ii-120.2
problems involving division and any of the
other operations of decimals, mixed
decimals, and whole numbers including
money using appropriate problem solving
Week 10
M6NS-Ij-120.3
Q2 demonstrates
understanding of
order of
operations, ratio
and proportion,
percent,
exponents, and
integers.
is able to apply
knowledge of order of
operations, ratio and
proportion, percent,
exponents, and
integers in
mathematical
situations.
expresses one value as a fraction of
another given their ratio and vice versa.
Week 1
M6NS-IIa-129
defines and illustrates the meaning of ratio
and proportion using concrete or pictorial
models.
M6NS-IIb-131
finds a missing term in a proportion (direct,
inverse, and partitive).
Week 2
M6NS-IIb-133
solves problems involving direct
proportion, partitive proportion, and
inverse proportion in different contexts
such as distance, rate, and time using
appropriate strategies and tools.
M6NS-IIc-134
finds the percentage or rate or percent in a
given problem.
Week 3
M6NS-IId-142
involving finding the percentage, rate and
base using appropriate strategies and tools.
M6NS-IId-143

40
The learner…
Performance
Standards
The learner…
The learner…
solves percent problems such as percent of
increase/decrease (discounts, original
price, rate of discount, sale price, marked-
up price), commission, sales tax, and simple
interest.
Week 4
M6NS-IIe-144
describes the exponent and the base in a
number expressed in exponential notation.
Week 5
M6NS-IIf-146
gives the value of numbers expressed in
exponential notation.
M6NS-IIf-147
interprets and explains the Grouping,
Exponent, Multiplication, Division,
Addition, Subtraction (GEMDAS) rule.
Week 6
M6NS-IIf-148
performs two or more different operations
on whole numbers with or without
exponents and grouping symbols.
M6NS-IIf-149
describe the set of integers and identify
real-life situations that make use of it.
Week 7
compares integers with other numbers
such as whole numbers, fractions, and
decimals.
M6NS-IIg-152
compares and arranges integers on the
number line.
Week 8
describes and interprets the basic
operations on integers using materials such
as algebra tiles, counters, chips, and cards.
M6NS-IIh-155
performs the basic operations on integers. Week 9 M6NS-IIi-156
involving basic operations of integers using
appropriate strategies and tools.
Week 10
M6NS-IIj-157

41
The learner…
Performance
Standards
The learner…
The learner…
Q3 demonstrates
understanding of
solid figures.
is able to construct
and describe the
different solid figures:
cube, prism, pyramid,
cylinder, cone, and
sphere.
visualizes and describes the different solid
figures: cube, prism, pyramid, cylinder,
cone, and sphere using various concrete
and pictorial models.
Week 1
differentiates solid figures from plane
figures.
M6GE-IIIa-28
identifies the faces of a solid figure. M6GE-IIIb-30
demonstrates
understanding of
sequence in
forming rules,
expressions and
equations.
is able to apply
knowledge of
sequence, expressions,
and equations in
mathematical
situations.
formulates the rule in finding the nth
term using different strategies (looking
for a pattern, guessing and checking,
working backwards)
e.g. 4,7,13,16,…n (the nth term is
3n+1)
Week 2
M6AL-IIId-7
differentiates expression from equation. M6AL-IIId-15
gives the translation of real-life verbal
expressions and equations into letters or
symbols and vice versa.
Week 3
M6AL-IIIe-16
defines a variable in an algebraic
expression and equation.
M6AL-IIIe-17
represents quantities in real-life situations
using algebraic expressions and
equations.
Week 4
M6AL-IIIe-18
involving different types of numerical
expressions and equations such as 7+ 9
=___ + 6.
M6AL-IIIf-19
demonstrates
understanding of
rate and speed,
is able to apply
knowledge of speed,
area, and surface area
calculates speed, distance, and time. Week 5 M6ME-IIIg-17
solves problems involving average rate
and speed.
M6ME-IIIg-18

42
The learner…
Performance
Standards
The learner…
The learner…
and of area and
surface area of
plane and
solid/space figures.
of plane and
solid/space figures in
mathematical
situations
finds the area of composite figures
formed by any two or more of the
following: triangle, square, rectangle,
circle, and semi-circle.
Week 6
M6ME-IIIh-89
involving area of composite figures
formed by any two or more of the
following: triangle, square, rectangle,
circle, and semi-circle.
M6ME-IIIh-90
visualizes and describes surface area and
names the unit of measure used for
measuring the surface area of solid/space
figures.
Week 7
M6ME-IIIi-91
finds the surface area of cubes, prisms,
pyramids, cylinders, cones, and spheres.
Week 8
M6ME-IIIi-93
solves word problems involving
measurement of surface area.
Week 9
M6ME-IIIj-94
Q4 demonstrates
understanding of
volume of solid
figures and meter
reading.
is able to apply
knowledge of volume
of solid figures and
meter reading in
mathematical
situations.
determines the relationship of the volume
between a rectangular prism and a
pyramid; a cylinder and a cone; and a
cylinder and sphere.
Week 1 M6ME-IVa-95
finds the volume of cylinders, pyramids,
cones, and spheres.
Week 2
M6ME-IVb-97
involving volumes of solids.
M6ME-IVc-98
reads and interprets electric and water
meter readings.
Week 3
M6ME-IVd-100
involving electric and water consumption.
M6ME-IVd-101

43
The learner…
Performance
Standards
The learner…
The learner…
demonstrates
understanding of
pie graphs and
experimental
probability.
interpret
representations of
data (tables and pie
graphs) and apply
experimental
probability in
mathematical
situations.
constructs a pie graph based on a given
set of data and interpret it.
Week 4
using data presented in a pie graph.
Week 5
M6SP-IVf-4.6
describes the meaning of probability such
as 50% chance of rain and one in a million
chance of winning.
Week 6 M6SP-IVg-19
performs experiments and records
outcomes.
M6SP-IVh-21
makes listings and diagrams of outcomes
and tells the number of favorable
outcomes and chances using these listings
and diagrams.
Week 7
M6SP-IVi-22
makes simple predictions of events based
on the results of experiments.
Week 8
M6SP-IVi-23
involving experimental and theoretical
probability.
Week 9
M6SP-IVj-24

44
The learner…
Performance
Standards
The learner…
The learner…
Q1 demonstrates
understanding of
key concepts of sets
and the real
number system.
is able to
formulate
challenging
situations
involving sets
and real
numbers and
solve these in
a variety of
strategies.
illustrates well-defined sets, subsets, universal sets,
null set, cardinality of sets, union and intersection of
sets and the different of two sets
Week 1
solves problems involving sets with the use of Venn
Diagram.
Week 2
represents the absolute value of a number on a
number line as the distance of a number from 0.
Week 3 M7NS-Ic-1
performs fundamental operations on integers. M7NS-Ic-d-1
illustrates the different properties of operations on
the set of integers.
Week 4 M7NS-Id-2
expresses rational numbers from fraction form to
decimal form and vice versa.
M7NS-Ie-1
performs operations on rational numbers Week 5 M7NS-If-1
describes principal roots and tells whether they are
rational or irrational.
Week 6 M7NS-Ig-1
determines between what two integers the square
root of a number is.
M7NS-Ig-2
estimates the square root of a whole number to the
nearest hundredth.
Week 7 M7NS-Ig-3
plots irrational numbers (up to square roots) on a
number line.***
M7NS-Ig-4
illustrates the different subsets of real numbers. Week 8 M7NS-Ih-1
arranges real numbers in increasing or decreasing
order and on a number line.
writes numbers in scientific notation and vice versa. Week 9 M7NS-Ii-1

45
The learner…
Performance
Standards
The learner…
The learner…
represents real-life situations and solves problems
involving real numbers.
Q2 demonstrates
understanding of
the key concepts of
measurement.
is able to
formulate
real-life
problems
involving
measurements
and solve
these using a
variety of
strategies.
approximates the measures of quantities particularly
length , weight/mass, volume, time, angle and
temperature and rate.
Week 1 M7ME-IIa-3
converts measurements from one unit to another in
both Metric and English systems.
Week 2 M7ME-IIb-1
solves problems involving conversion of units of
measurement.
M7ME-IIb-2
demonstrates
understanding of
key concepts of
algebraic
expressions, the
properties of real
numbers as applied
in linear equations,
and inequalities in
one variable.
is able to
model
situations
using oral,
written,
graphical, and
algebraic
methods in
solving
problems
involving
algebraic
expressions,
linear
equations, and
translates English phrases to mathematical phrases
and English sentences to mathematics sentences, and
vice versa.
Week 3
Illustrates and differentiates related terms in algebra:
a. where is a positive integer
b. constants and variables
c. literal coefficients and numerical coefficients
d. algebraic expressions, terms and polynomials
e. number of terms, degree of the term and degree of
the polynomial.
evaluates algebraic expressions for given values of
the variables.
Week 4 M7AL-IIc-4
adds and subtracts polynomials. M7AL-IId-2
derives the laws of exponent. Week 5 M7AL-IId-e-1
multiplies and divides polynomials. M7AL-IIe-2
uses models and algebraic methods to find the: (a)
product of two binomials; (b) product of the sum and
Week 6 M7AL-IIe-g-1
n
a n

46
The learner…
Performance
Standards
The learner…
The learner…
inequalities in
one variable.
difference of two terms; (c) square of a binomial; (d)
cube of a binomial; (e) product of a binomial and a
trinomial.
solves problems involving algebraic expressions. Week 7 to 8 M7AL-IIg-2
differentiates algebraic expressions, equations and
inequalities.
illustrates linear equation and inequality in one
variable.
M7AL-IIh-4
finds the solution of linear equation or inequality in
one variable.
Week 9 M7AL-IIi-1
solves linear equation or inequality in one variable
involving absolute value by: (a) graphing; and (b)
algebraic methods.
M7AL-IIi-j-1
solves problems involving equations and inequalities
in one variable.
M7AL-IIj-2
Q3 demonstrates
understanding of
key concepts of
geometry of shapes
and sizes, and
geometric
relationships.
is able to
create models
of plane
figures and
formulate and
solve
accurately
authentic
problems
involving sides
represents point, line and plane using concrete and
pictorial models.
Week 1 M7GE-IIIa-1
illustrates subsets of a line. M7GE-IIIa-2
classifies the different kinds of angles. M7GE-IIIa-3
derives relationships of geometric figures using
measurements and by inductive reasoning;
supplementary angles, complementary angles,
congruent angles, vertical angles, adjacent angles,
linear pairs, perpendicular lines, and parallel lines.
Week 2 M7GE-IIIb-1
derives relationships among angles formed by
parallel lines cut by a transversal using measurement
and by inductive reasoning.
Week 3 M7GE-IIIc-1

47
The learner…
Performance
Standards
The learner…
The learner…
and angles of
a polygon
uses a compass and straightedge to bisect line
segments and angles and construct perpendiculars
and parallels.
Week 4 M7GE-IIId-e-1
illustrates polygons: (a) convexity; (b) angles; and (c)
sides.
Week 5 M7GE-IIIe-2
derives inductively the relationship of exterior and
interior angles of a convex polygon.
Week 6 M7GE-IIIf-1
illustrates a circle and the terms related to it: radius,
diameter chord, center, arc, chord, central angle, and
inscribed angle.
Week 7 M7GE-IIIg-1
constructs triangles, squares, rectangles, regular
pentagons, and regular hexagons.
Week 8 M7GE-IIIh-i-1
solves problems involving sides and angles of a
polygon.
Week 9 M7GE-IIIj-1
Q4 demonstrates
understanding of
key concepts, uses
and importance of
Statistics, data
collection/gathering
and the different
forms of data
representation,
measures of central
tendency, measures
of variability, and
probability.
is able to
collect and
organize data
systematically
and compute
accurately
measures of
central
tendency and
variability and
apply these
appropriately
in data
analysis and
poses real-life problems that can be solved by
Statistics.
Week 1 M7SP-IVa-2
formulates simple statistical instruments. M7SP-IVa-3
gathers statistical data. Week 2 M7SP-IVb-1
organizes data in a frequency distribution table. Week 3 M7SP-IVc-1
uses appropriate graphs to represent organized data:
pie chart, bar graph, line graph, histogram, and
ogive.
Week 4 to 5
M7SP-IVd-e-1
illustrates the measures of central tendency (mean,
median, and mode) of a statistical data.
Week 6 M7SP-IVf-1
calculates the measures of central tendency of
ungrouped and grouped data.
M7SP-IVf-g-1
illustrates the measures of variability (range, average
deviation, variance, standard deviation) of a
statistical data.
Week 7 M7SP-IVh-1

48
The learner…
Performance
Standards
The learner…
The learner…
interpretation
in different
fields.
calculates the measures of variability of grouped and
ungrouped data.
M7SP-IVh-i-1
uses appropriate statistical measures in analyzing and
interpreting statistical data.
Week 8 to 9 M7SP-IVj-1
draws conclusions from graphic and tabular data and
measures of central tendency and variability.
M7SP-IVj-2
Quarter Content
Standards
The learner…
Performance
Standards
The learner…
The learner…
Q1 demonstrates
understanding of
key concepts of
factors of
polynomials,
rational algebraic
expressions, linear
equations and
inequalities in two
variables, systems
of linear equations
and inequalities in
is able to
formulate real-
life problems
involving factors
of polynomials,
rational
algebraic
expressions,
linear equations
and inequalities
in two variables,
systems of
factors completely different types of polynomials
(polynomials with common monomial factor,
difference of two squares, sum and difference of two
cubes, perfect square trinomials, and general
trinomials).
Week 1 to 2 M8AL-Ia-b-1
solves problems involving factors of polynomials. M8AL-Ib-2
illustrates rational algebraic expressions.
Week 3 M8AL-Ic-1
simplifies rational algebraic expressions. M8AL-Ic-2

49
Quarter Content
Standards
The learner…
Performance
Standards
The learner…
The learner…
two variables and
linear functions.
linear equations
and inequalities
in two variables
and linear
functions, and
solve these
problems
accurately using
a variety of
strategies.
performs operations on rational algebraic
expressions.
Week 4 M8AL-Ic-d-1
solves problems involving rational algebraic
expressions.
M8AL-Id-2
illustrates the rectangular coordinate system and its
uses.
Week 5 M8AL-Ie-1
illustrates linear equations in two variables. M8AL-Ie-3
Illustrates and finds the slope of a line given two
points, equation, and graph.
writes the linear equation in the form
and vice versa.
Week 6 M8AL-If-1
graphs a linear equation given (a) any two points; (b)
the – and – intercepts; (c) the slope and a point
on the line.
M8AL-If-2
describes the graph of a linear equation in terms of its
intercepts and slope.
M8AL-If-3
finds the equation of a line given (a) two points; (b)
the slope and a point; (c) the slope and its intercepts.
Week 7 M8AL-Ig-1
solves problems involving linear equations in two
variables.
M8AL-Ig-2
illustrates a system of linear equations in two
variables.
Week 8 M8AL-Ih-1
graphs a system of linear equations in two variables. M8AL-Ih-2
categorizes when a given system of linear equations
in two variables has graphs that are parallel,
intersecting, and coinciding.
M8AL-Ih-3
c
by
ax 

b
mx
y 

x y

50
Quarter Content
Standards
The learner…
Performance
Standards
The learner…
The learner…
solves problems involving systems of linear equations
in two variables by (a) graphing; (b) substitution; (c)
elimination.
Week 9
Q2 demonstrates key
concepts of linear
inequalities in two
variables, systems
of linear
inequalities in two
variables and
linear functions.
is able to
formulate and
solve accurately
real-life
problems
involving linear
inequalities in
two variables,
systems of
linear
inequalities in
two variables,
and linear
functions.
differentiates linear inequalities in two variables from
linear equations in two variables.
Week 1 M8AL-IIa-2
Illustrates and graphs linear inequalities in two
variables.
solves problems involving linear inequalities in two
variables.
M8AL-IIa-4
solves problems involving systems of linear
inequalities in two variables.
Week 2 M8AL-IIb-2
illustrates a relation and a function. Week 3 M8AL-IIc-1
verifies if a given relation is a function. M8AL-IIc-2
determines dependent and independent variables. M8AL-IIc-3
finds the domain and range of a function. Week 4 M8AL-IId-1
graphs and illustrates a linear function and its (a)
domain; (b) range; (c) table of values; (d) intercepts;
and (e) slope.
solves problems involving linear functions. Week 5 M8AL-IIe-2
demonstrates
understanding of
key concepts of
logic and
reasoning.
is able to
communicate
mathematical
thinking with
coherence and
clarity in
formulating and
determines the relationship between the hypothesis
and the conclusion of an if-then statement.
Week 6 M8GE-IIf-1
transforms a statement into an equivalent if-then
statement.
M8GE-IIf-2
determines the inverse, converse, and contrapositive
of an if-then statement.
Week 7 M8GE-IIg-1
illustrates the equivalences of: (a) the statement and
its contrapositive; and (b) the converse and inverse of
a statement.
Week 8 M8GE-IIg-2

51
Quarter Content
Standards
The learner…
Performance
Standards
The learner…
The learner…
analyzing
arguments.
uses inductive or deductive reasoning in an argument. Week 9 M8GE-IIh-1
writes a proof (both direct and indirect).
M8GE-IIi-j-1
Q3 demonstrates
understanding of
key concepts of
axiomatic
structure of
geometry and
triangle
congruence.
1. is able to
formulate an
organized plan
to handle a real-
life situation.
2. is able to
communicate
mathematical
thinking with
coherence and
clarity in
formulating,
investigating,
analyzing, and
solving real-life
problems
involving
congruent
triangles using
appropriate and
accurate
representations.
describes a mathematical system. Week 1 to 2 M8GE-IIIa-1
illustrates the need for an axiomatic structure of a
mathematical system in general, and in Geometry in
particular: (a) defined terms; (b) undefined terms; (c)
postulates; and (d) theorems.
M8GE-IIIa-c-1
illustrates triangle congruence. Week 3 to 4 M8GE-IIId-1
illustrates the SAS, ASA and SSS congruence
postulates.
M8GE-IIId-e-1
solves corresponding parts of congruent triangles Week 5 M8GE-IIIf-1
proves two triangles are congruent. Week 6 M8GE-IIIg-1
proves statements on triangle congruence. Week 7 M8GE-IIIh-1
applies triangle congruence to construct
perpendicular lines and angle bisectors.
Week 8 to 9 M8GE-IIIi-j-1
Q4 demonstrates
understanding of
key concepts of
is able to
communicate
mathematical
illustrates theorems on triangle inequalities (Exterior
Angle Inequality Theorem, Triangle Inequality
Theorem, Hinge Theorem).
Week 1 M8GE-IVa-1

52
Quarter Content
Standards
The learner…
Performance
Standards
The learner…
The learner…
inequalities in a
triangle, and
parallel and
perpendicular
lines.
thinking with
coherence and
clarity in
formulating,
investigating,
analyzing, and
solving real-life
problems
involving
triangle
inequalities, and
parallelism and
perpendicularity
of lines using
appropriate and
accurate
representations.
applies theorems on triangle inequalities. Week 2 M8GE-IVb-1
proves inequalities in a triangle. Week 3 M8GE-IVc-1
proves properties of parallel lines cut by a transversal.
Week 4
M8GE-IVd-1
determines the conditions under which lines and
segments are parallel or perpendicular.
Week 5 M8GE-IVe-1
demonstrates
understanding of
key concepts of
probability.
is able to
formulate and
solve practical
problems
involving
probability of
simple events.
illustrates an experiment, outcome, sample space and
event.
Week 6 M8GE-IVf-1
counts the number of occurrences of an outcome in
an experiment: (a) table; (b) tree diagram; (c)
systematic listing; and (d) fundamental counting
principle.
Week 7 M8GE-IVf-g-1
finds the probability of a simple event. Week 8 M8GE-IVh-1
illustrates an experimental probability and a
theoretical probability.
Week 9 M8GE-IVi-1
solves problems involving probabilities of simple
events.
M8GE-IVi-j-1

53
Quarter Content
Standards
The learner…
Performance
Standards
The learner…
The learner…
Q1 demonstrates
understanding
of key
concepts of
quadratic
equations,
inequalities
and functions,
and rational
algebraic
equations.
is able to
investigate
thoroughly
mathematical
relationships in
various situations,
formulate real-life
problems
involving
quadratic
equations,
inequalities and
functions, and
rational algebraic
equations and
solve them using
a variety of
strategies.
illustrates quadratic equations. Week 1 M9AL-Ia-1
solves quadratic equations by: (a) extracting square
roots; (b) factoring; (c) completing the square; and (d)
using the quadratic formula.
M9AL-Ia-b-1
characterizes the roots of a quadratic equation using
the discriminant.
Week 2 to 3 M9AL-Ic-1
describes the relationship between the coefficients
and the roots of a quadratic equation.
M9AL-Ic-2
solves equations transformable to quadratic equations
(including rational algebraic equations).
M9AL-Ic-d-1
solves problems involving quadratic equations and
rational algebraic equations.
Week 4
M9AL-Ie-1
illustrates quadratic inequalities Week 5 M9AL-If-1
solves quadratic inequalities. M9AL-If-2
solves problems involving quadratic inequalities. M9AL-If-g-1
models real-life situations using quadratic functions. Week 6 M9AL-Ig-2
represents a quadratic function using: (a) table of
values; (b) graph; and (c) equation.
M9AL-Ig-3
transforms the quadratic function definedbyy=ax2+ bx+
cintotheformy=a(x–h)2 +k.
Week 7 to 8 M9AL-Ih-1

54
Quarter Content
Standards
The learner…
Performance
Standards
The learner…
The learner…
graphs a quadratic function: (a) domain; (b) range; (c)
intercepts; (d) axis of symmetry; (e) vertex; (f)
direction of the opening of the parabola. M9AL-Ig-h-i-1
analyzes the effects of changing the values of a, h and k
in the equation y = a(x – h)2 + k of a quadratic function
on its graph.
M9AL-Ii-2
determines the equation of a quadratic function given:
(a) a table of values; (b) graph; (c) zeros.
Week 9 M9AL-Ij-1
solves problems involving quadratic functions. M9AL-Ii-j-2
Q2 demonstrates
understanding
of key
concepts of
variation and
radicals.
is able to
formulate and
solve accurately
problems
involving radicals.
illustrates situations that involve the following
variations: (a) direct; (b) inverse; (c) joint; (d) combined.
Week 1 to 2 M9AL-IIa-1
translates into variation statement a relationship
between two quantities given by: (a) a table of values;
(b) a mathematical equation; (c) a graph, and vice
versa.
M9AL-IIa-b-1
solves problems involving variation. M9AL-IIb-c-1
applies the laws involving positive integral exponents
to zero and negative integral exponents.
Week 3 M9AL-IId-1
simplifies expressions with rational exponents. Week 4 M9AL-IIe-1
writes expressions with rational exponents as radicals
and vice versa.
M9AL-IIf-1
derives the laws of radicals. Week 5 M9AL-IIf-2
simplifies radical expressions using the laws of radicals. Week 6 M9AL-IIg-1
performs operations on radical expressions. Week 7 M9AL-IIh-1
solves equations involving radical expressions. Week 8 M9AL-IIi-1
solves problems involving radicals. Week 9 M9AL-IIj-1
Q3 determines the conditions that make a quadrilateral a
parallelogram.
Week 1
M9GE-IIIa-2

55
Quarter Content
Standards
The learner…
Performance
Standards
The learner…
The learner…
demonstrates
understanding
of key
concepts of
parallelograms
and triangle
similarity.
is able to
investigate,
analyze, and solve
problems
involving
parallelograms
and triangle
similarity through
appropriate and
accurate
representation.
uses properties to find measures of angles, sides and
other quantities involving parallelograms. M9GE-IIIb-1
provestheoremsonthedifferentkindsofparallelogram
(rectangle,rhombus,square).
Week 2 M9GE-IIIc-1
proves the Midline Theorem. Week 3 M9GE-IIId-1
proves theorems on trapezoids and kites. M9GE-IIId-2
solves problems involving parallelograms, trapezoids
and kites.
Week 4 M9GE-IIIe-1
describes a proportion. Week 5 M9GE-IIIf-1
appliesthefundamentaltheoremsofproportionalitytosolve
problemsinvolvingproportions.
M9GE-IIIf-2
illustrates similarity of figures. Week 6 to 7 M9GE-IIIg-1
proves the conditions for similarity of triangles.
1.1 SAS similarity theorem
1.2 SSS similarity theorem
1.3 AA similarity theorem
1.4 right triangle similarity theorem
1.5 special right triangle theorems
M9GE-IIIg-h-1
applies the theorems to show that given triangles are
similar.
Week 8 M9GE-IIIi-1
proves the Pythagorean Theorem. M9GE-IIIi-2
solves problems that involve triangle similarity and
right triangles.
Week 9

56
Quarter Content
Standards
The learner…
Performance
Standards
The learner…
The learner…
M9GE-IIIj-1
Q4 demonstrates
understanding
of the basic
concepts of
trigonometry.
is able to apply
the concepts of
trigonometric
ratios to
formulate and
solve real-life
problems with
precision and
accuracy.
illustrates the six trigonometric ratios: sine, cosine,
tangent, secant, cosecant, and cotangent.
Week 1 to 2
M9GE-IVa-1
finds the trigonometric ratios of special angles. M9GE -IVb-c-1
illustrates angles of elevation and angles of depression.
Week 3 to 5
M9GE-IVd-1
uses trigonometric ratios to solve real-life problems
involving right triangles.
M9GE-IVe-1
illustrates laws of sines and cosines.
Week 6 to 9
M9GE-IVf-g-1
solves problems involving oblique triangles.
M9GE-IVh-j-1

57
Quarter Content
Standards
The learner…
Performance
Standards
The learner…
The learner…
Q1 demonstrates
understanding
of key
concepts of
sequences,
polynomials
and
polynomial
equations.
is able to
formulate and
solve problems
involving
sequences,
polynomials and
polynomial
equations in
different
disciplines
through
appropriate and
accurate
representations.
generates patterns. Week 1 to 2 M10AL-Ia-1
illustrates an arithmetic sequence M10AL-Ib-1
determines arithmetic means, nth term of an
arithmetic sequence and sum of the terms of a given
arithmetics sequence.
illustrates a geometric sequence. Week 3 M10AL-Id-1
differentiates a geometric sequence from an arithmetic
sequence.
M10AL-Id-2
determines geometric means, nth term of a geometric
sequence and sum of the terms of a given finite or
infinite geometric sequence
Week 4
solves problems involving sequences. Week 5 M10AL-If-2
performs division of polynomials using long division
and synthetic division.
Week 6
M10AL-Ig-1
proves the Remainder Theorem, Factor Theorem and
the Rational Root Theorem.
factors polynomials. Week 7 M10AL-Ih-1
illustrates polynomial equations. Week 8 M10AL-Ii-1
solves problems involving polynomials and polynomial
equations.
Week 9 M10AL-Ij-2
Q2 demonstrates
understanding
of key
concepts of
is able to conduct
systematically a
mathematical
investigation
involving
illustrates polynomial functions. Week 1 to 2 M10AL-IIa-1
understand, describe and interpret the graphs
polynomial functions.
solves problems involving polynomial functions.
M10AL-IIb-2

58
Quarter Content
Standards
The learner…
Performance
Standards
The learner…
The learner…
polynomial
function.
polynomial
functions in
different fields.
demonstrates
understanding
of key
concepts of
circles and
coordinate
geometry.
1. is able to
formulate and
find solutions to
challenging
situations
involving circles
and other related
terms in different
disciplines
through
appropriate and
accurate
representations.
2. is able to
formulate and
solve problems
involving
geometric figures
on the
rectangular
coordinate plane
with
perseverance and
accuracy.
derives inductively the relations among chords, arcs,
central angles, and inscribed angles.
Week 3 to 4
M10GE-IIc-1
proves theorems related to chords, arcs, central angles,
and inscribed angles.
M10GE-IIc-d-1
illustrates secants, tangents, segments, and sectors of a
circle.
Week 5 to 6
M10GE-IIe-1
proves theorems on secants, tangents, and segments. M10GE-IIe-f-1
solves problems on circles. M10GE-IIf-2
applies the distance formula to prove some geometric
properties.
Week 7 M10GE-IIg-2
illustrates the center-radius form of the equation of a
circle.
Week 8 M10GE-IIh-1
determines the center and radius of a circle given its
equation and vice versa.
M10GE-IIh-2
graphs and solves problems involving circles and other
geometric figures on the coordinate plane.
Week 9
Q3 illustrates the permutation of objects. Week 1 to 2 M10SP-IIIa-1

59
Quarter Content
Standards
The learner…
Performance
Standards
The learner…
The learner…
demonstrates
understanding
of key
concepts of
combinatorics
and
probability.
is able to use
precise counting
technique and
probability in
formulating
conclusions and
making decisions.
solves problems involving permutations M10SP-IIIb-1
illustrates the combination of objects. Week 3 to 4 M10SP-IIIc-1
differentiates permutation from combination of
objects taken at a time.
M10SP-IIIc-2
solves problems involving permutations and
combinations
Week 5 M10SP-IIId-e-1
illustrates events, and union and intersection of events. Week 6 M10SP-IIIf-1
illustrates the probability of a union of two events. Week 7 M10SP-IIIg-1
findsthe probability of . Week 8 M10SP-IIIg-h-1
illustrates mutuallyexclusive events. Week 9 M10SP-IIIi-1
solves problems involving probability. M10SP-IIIi-j-1
Q4 demonstrates
understanding
of key
concepts of
measures of
position.
is able to conduct
systematically a
mini-research
applying the
different
statistical
methods.
illustrates the following measures of position: quartiles,
deciles and percentiles.
Week 1 M10SP-IVa-1
calculates a specified measure of position (e.g. 90th
percentile) of a set of data.
Week 2 M10SP-IVb-1
interprets measures of position. Week 3 M10SP-IVc-1
solves problems involving measures of position. Week 4 to 5 M10SP-IVd-e-1
formulates statistical mini-research.
Week 6 to 7
M10SP-IVf-g-1
uses appropriate measures of position and other
statistical methods in analyzing and interpreting
research data.
Week 8 to 9
M10SP-IVh-j-1
n
r
 
B
A

60
Department of Education
Bureau of Curriculum Development
Curriculum Standards Development Division
Meralco Avenue, Pasig City
SENIOR HIGH SCHOOL
MATH SUBJECTS
Most Essential Learning Competencies
School Year 2020-2021
May 2020

61
Subject: General Mathematics
The learner
demonstrates
understanding of…
Performance Standards
The learner is able to…
The learner…
Q1 key concepts of
functions.
accurately construct
mathematical models
to represent real-life
situations using
functions.
represents real-life situations using functions,
including piece-wise functions.
Week 1 M11GM-Ia-1
evaluates a function. M11GM-Ia-2
performs addition, subtraction, multiplication,
division, and composition of functions
M11GM-Ia-3
solves problems involving functions. M11GM-Ia-4
key concepts of
rational functions.
accurately formulate
and solve real-life
problems involving
rational functions.
represents real-life situations using rational
functions.
Week 2 M11GM-Ib-1
distinguishes rational function, rational
equation, and rational inequality.
M11GM-Ib-2
solves rational equations and inequalities. M11GM-Ib-3
represents a rational function through its: (a)
table of values, (b) graph, and (c) equation.
M11GM-Ib-4
finds the domain and range of a rational
function.
M11GM-Ib-5
determines the: (a) intercepts; (b) zeroes; and (c)
asymptotes of rational functions
Week 3 M11GM-Ic-1
solves problems involving rational functions,
equations, and inequalities.
M11GM-Ic-3
key concepts of
inverse functions,
exponential
functions, and
apply the concepts of
inverse functions,
exponential functions,
and logarithmic
functions to formulate
represents real-life situations using one-to one
functions.
Week 4 M11GM-Id-1
determines the inverse of a one-to-one function. M11GM-Id-2
represents an inverse function through its: (a)
table of values, and (b) graph.
M11GM-Id-3

62
The learner
demonstrates
understanding of…
The learner…
logarithmic
functions.
and solve real-life
problems with precision
and accuracy.
finds the domain and range of an inverse
function.
M11GM-Id-4
solves problems involving inverse functions. Week 5 M11GM-Ie-2
represents real-life situations using exponential
functions.
M11GM-Ie-3
distinguishes between exponential function,
exponential equation, and exponential
inequality.
M11GM-Ie-4
solves exponential equations and inequalities. Week 6 M11GM-Ie-f-1
represents an exponential function through its:
(a) table of values, (b) graph, and (c) equation.
M11GM-If-2
finds the domain and range of an exponential
function.
M11GM-If-3
determinestheintercepts,zeroes,and asymptotesof
anexponentialfunction.
M11GM-If-4
solves problems involving exponential functions,
Week 7 M11GM-Ig-2
represents real-life situations using logarithmic
functions.
Week 8 M11GM-Ih-1
distinguishes logarithmic function, logarithmic
equation, and logarithmic inequality.
M11GM-Ih-2
solves logarithmic equations and inequalities. M11GM-Ih-i-1
represents a logarithmic function through its: (a)
table of values, (b) graph, and (c) equation.
Week 9 M11GM-Ii-2
finds the domain and range of a logarithmic
function.
M11GM-Ii-3

63
The learner
demonstrates
understanding of…
The learner…
determines the intercepts, zeroes, and
asymptotes of logarithmic functions.
M11GM-Ii-4
solves problems involving logarithmic functions,
Week 10 M11GM-Ij-2
Q2 key concepts of
simple and
compound
interests, and
simple and general
annuities.
investigate, analyze and
solve problems
involving simple and
compound interests and
simple and general
annuities using
appropriate business
and financial
instruments.
illustrates simple and compound interests. Week 1 to 2 M11GM-IIa-1
distinguishes between simple and compound
interests.
M11GM-IIa-2
computes interest, maturity value, future value,
and present value in simple interest and
compound interest environment.
M11GM-IIa-b-1
solves problems involving simple and compound
interests.
M11GM-IIb-2
illustrates simple and general annuities. Week 3 to 4 M11GM-IIc-1
distinguishes between simple and general
annuities.
M11GM-IIc-2
finds the future value and present value of both
simple annuities and general annuities.
M11GM-IIc-d-1
calculates the fair market value of a cash flow
stream that includes an annuity.
M11GM-IId-2
calculates the present value and period of
deferral of a deferred annuity.
M11GM-IId-3
basic concepts of
stocks and bonds.
use appropriate
financial instruments
involving stocks and
bonds in formulating
conclusions and making
decisions.
illustrate stocks and bonds. Week 5 M11GM-IIe-1
distinguishes between stocks and bonds. M11GM-IIe-2
describes the different markets for stocks and
bonds.
M11GM-IIe-3
analyzes the different market indices for stocks
and bonds.
M11GM-IIe-4

64
The learner
demonstrates
understanding of…
The learner…
basic concepts of
business and
consumer loans.
decide wisely on the
appropriateness of
business or consumer
loan and its proper
utilization.
illustrates business and consumer loans. Week 6 M11GM-IIf-1
distinguishes between business and consumer
loans.
M11GM-IIf-2
solves problems involving business and
consumer loans (amortization, mortgage).
M11GM-IIf-3
key concepts of
propositional logic;
syllogisms and
fallacies.
judiciously apply logic in
real-life arguments.
illustrates and symbolizes propositions. Week 7
distinguishes between simple and compound
propositions.
M11GM-IIg-3
performs the different types of operations on
propositions.
M11GM-IIg-4
determines the truth values of propositions. Week 8 M11GM-IIh-1
illustrates the different forms of conditional
propositions.
M11GM-IIh-2
illustrates different types of tautologies and
fallacies.
Week 9 M11GM-IIi-1
key methods of
proof and disproof.
appropriately apply a
method of proof and
disproof in real-life
situations.
determines the validity of categorical syllogisms. M11GM-IIi-2
establishes the validity and falsity of real-life
arguments using logical propositions, syllogisms,
and fallacies.
M11GM-IIi-3

65
Grade Level: Grade 11/12
Subject: Statistics and Probability
The learner
demonstrates
understanding of…
Performance
Standards
The learner…
Q3 The learner
demonstrates
understanding of
key concepts of
random variables
and probability
distributions.
The learner is able
to apply an
appropriate random
variable for a given
real-life problem
(such as in decision
making and games
of chance).
illustrates a random variable (discrete and
continuous).
Week 1 M11/12SP-IIIa-1
distinguishes between a discrete and a continuous
random variable.
M11/12SP-IIIa-2
finds the possible values of a random variable. M11/12SP-IIIa-3
illustrates a probability distribution for a discrete
random variable and its properties.
M11/12SP-IIIa-4
computes probabilities corresponding to a given
random variable.
Week 2 M11/12SP-IIIa-6
illustrates the mean and variance of a discrete
random variable.
M11/12SP-IIIb-1
calculates the mean and the variance of a discrete
random variable.
M11/12SP-IIIb-2
interprets the mean and the variance of a discrete
random variable.
Week 3 M11/12SP-IIIb-3
solves problems involving mean and variance of
probability distributions.
M11/12SP-IIIb-4
The learner
demonstrates
understanding of
key concepts of
normal
The learner is able
to accurately
formulate and solve
real-life problems in
different disciplines
illustrates a normal random variable and its
characteristics.
M11/12SP-IIIc-1
identifies regions under the normal curve
corresponding to different standard normal values.
Week 4 M11/12SP-IIIc-3
converts a normal random variable to a standard
normal variable and vice versa.
M11/12SP-IIIc-4

66
The learner
demonstrates
understanding of…
Performance
Standards
The learner…
probability
distribution.
involving normal
distribution.
computes probabilities and percentiles using the
standard normal table.
M11/12SP-IIIc-d-1
The learner
demonstrates
understanding of
key concepts of
sampling and
sampling
distributions of the
sample mean.
The learner is able to
apply suitable
sampling and sampling
distributions of the
sample mean to solve
different disciplines.
illustrates random sampling. Week 5 M11/12SP-IIId-2
distinguishes between parameter and statistic. M11/12SP-IIId-3
identifies sampling distributions of statistics (sample
mean).
M11/12SP-IIId-4
finds the mean and variance of the sampling
distribution of the sample mean.
Week 6 M11/12SP-IIId-5
defines the sampling distribution of the sample mean
for normal population when the variance is: (a)
known; (b) unknown
M11/12SP-IIIe-1
illustrates the Central Limit Theorem. Week 7
to 8
M11/12SP-IIIe-2
defines the sampling distribution of the sample mean
using the Central Limit Theorem.
M11/12SP-III-3
solves problems involving sampling distributions of
the sample mean.
M11SP-IIIe-f-1
The learner
demonstrates
understanding of
key concepts of
estimation of
population mean
and population
proportion.
estimate the
population mean and
population proportion
to make sound
inferences in real-life
problems in different
disciplines.
illustrates the t-distribution. Week 9 M11/12SP-IIIg-2
identifies percentiles using the t-table. M11/12SP-IIIg-5
identifies the length of a confidence interval. Week 10 M11/12SP-IIIj-1
computes for the length of the confidence interval. M11/12SP-IIIj-2
computes for an appropriate sample size using the
length of the interval.
M11/12SP-IIIj-3
solves problems involving sample size determination. M11/12SP-IIIj-4
Q4 The learner
demonstrates
understanding of
perform appropriate
tests of hypotheses
illustrates: (a) null hypothesis; (b) alternative
hypothesis; (c) level of significance; (d) rejection
region; and (e) types of errors in hypothesis testing.
Week 1 M11/12SP-IVa-1

67
The learner
demonstrates
understanding of…
Performance
Standards
The learner…
key concepts of
tests of hypotheses
on the population
mean and
population
proportion.
involving the
population mean and
population proportion
to make inferences in
different disciplines.
identifies the parameter to be tested given a real-life
problem.
M11/12SP-IVa-3
formulates the appropriate null and alternative
hypotheses on a population mean.
Week 2 M11/12SP-IVb-1
identifies the appropriate form of the test-statistic
when: (a) the population variance is assumed to be
known; (b) the population variance is assumed to be
unknown; and (c) the Central Limit Theorem is to be
used.
M11/12SP-IVb-2
identifies the appropriate rejection region for a given
level of significance when: (a) the population variance
is assumed to be known; (b) the population variance
is assumed to be unknown; and (c) the Central Limit
Theorem is to be used.
Week 3 M11/12SP-IVc-1
computes for the test-statistic value (population
mean).
Week 4 M11/12SP-IVd-1
draws conclusion about the population mean based
on the test-statistic value and the rejection region.
M11/12SP-IVd-2
solves problems involving test of hypothesis on the
population mean.
Week 5 M11/12SP-IVe-1
formulates the appropriate null and alternative
hypotheses on a population proportion.
M11/12SP-IVe-2
identifies the appropriate form of the test-statistic
when the Central Limit Theorem is to be used.
M11/12SP-IVe-3
identifies the appropriate rejection region for a given
level of significance when the Central Limit Theorem
is to be used.
Week 6 M11/12SP-IVe-4

68
The learner
demonstrates
understanding of…
Performance
Standards
The learner…
computes for the test-statistic value (population
proportion).
M11/12SP-IVf-1
draws conclusion about the population proportion
based on the test-statistic value and the rejection
region.
M11/12SP-IVf-2
solves problems involving test of hypothesis on the
population proportion.
Week 7 M11/12SP-IVf-g-1
The learner
demonstrates
understanding of
key concepts of
correlation and
regression
analyses.
perform correlation
and regression
analyses on real-life
problems in different
disciplines.
illustrates the nature of bivariate data. M11/12SP-IVg-2
constructs a scatter plot. M11/12SP-IVg-3
describes shape (form), trend (direction), and
variation (strength) based on a scatter plot.
M11/12SP-IVg-4
calculates the Pearson’s sample correlation
coefficient.
Week 8 M11/12SP-IVh-2
solves problems involving correlation analysis. M11/12SP-IVh-3
identifies the independent and dependent variables. Week 9 M11/12SP-IVi-1
calculates the slope and y-intercept of the regression
line.
M11/12SP-IVi-3
interprets the calculated slope and y-intercept of the
regression line.
M11/12SP-IVi-4
predicts the value of the dependent variable given
the value of the independent variable.
Week 10 M11/12SP-IVj-1
solves problems involving regression analysis. M11/12SP-IVj-2

69
Subject: Business Mathematics
The learners
demonstrate an
understanding of…
The learners are able to…
Most Essential Learning
competencies
The learner…
Q1 1. fractions
2. decimals and
percentage
1. Solve problems involving
fractions, decimals and percent
related to business
Express:
a. fractions to decimal and
percent forms
b. decimals to fractions and
percent forms
c. percent to fractions and
decimal forms
Week 1 to 2
Give real-life situations to
illustrate fractions, decimals,
and percent
ABM_BM11FO-Ic-4
Solve problems involving
fractions, decimals, and
percent
ABM_BM11FO-Id-5
key concepts of ratio and
proportion
1. formulate and solve problems
involving ratio and proportion
2. use the concept of proportion
in making life decisions
Identify the different kinds of
proportions and write
examples of real-life
situations for each
Week 3
direct, inverse and partitive
proportion
Week 4 ABM_BM11RP-If-4
key concepts in buying
and selling
Analyze and solve problems on
important factors in managing a
Differentiate Mark-on, Mark
down and Mark-up
Week 5 ABM_BM11BS-Ig-1

70
The learners
demonstrate an
understanding of…
competencies
The learner…
business: buying products and
selling products
obtain Mark-on, Mark-down,
and Mark-up given price of a
product
Differentiate mark-up from
margins
Week 6 ABM_BM11BS-Ih-3
Describe how gross margins
is used in sales
ABM_BM11BS-Ih-4
Compute single trade
discounts and discount series
Differentiate profit from loss Week 7 ABM_BM11BS-Ii-6
Illustrate how profit is
obtained and how to avoid
loss in a given transaction
ABM_BM11BS-Ii-7
Determine the break-even
point
Week 8
buying and selling products
ABM_BM11BS-Ij-9
Compute interest specifically
as applied to mortgage,
amortization, and on
services/utilities and on
deposits and loans
Week 9
Q2 Illustrate the different types
of commissions
Week 1 ABM_BM11BS-IIa-11
Compute commissions on
cash basis and commission
on instalment basis
ABM_BM11BS-IIa-12

71
The learners
demonstrate an
understanding of…
competencies
The learner…
Compute down payment,
gross balance and current
increased balance
interests and commissions
Week 2 ABM_BM11BS-IIb-14
the fundamental
operations of
mathematics as applied
in salaries and wages
apply appropriate mathematical
operation in computing salaries
and wages
Define salary, wage, income,
benefits
Week 3 ABM_BM11SW-IIc-1
Compute gross and net
earnings
ABM_BM11SW-IId-2
Define each of the benefits
given to wage earners
Week 4 ABM_BM11SW-IIe-5
Distinguish taxable from
nontaxable benefits
ABM_BM11SW-IIe-6
Enumerate the standard
deductions with the
corresponding computation
ABM_BM11SW- IIe-7
Identify the variables needed
in the computation of the
overtime
Week 5 ABM_BM11SW- IIe -8
Compute overtime pay ABM_BM11SW- IIe -9
Use E- spread sheet in the
computation of salary and
overtime pay
Week 6 ABM_BM11SW- IIf -10
Present graphical
representation of the details
or particulars of the salary.
ABM_BM11SW- IIf -13

72
The learners
demonstrate an
understanding of…
competencies
The learner…
business data present
them in graphs, charts,
and tables
solve problems in real-life
business situations, present
data in graphical form, and
analyze them
Compare the forms (textual,
tabular and graphical) of
business data.
Week 7 ABM_BM11PAD-IIg-2
Analyze and interprets the
data presented in the table
using measures of central
tendency and variability and
tests of significant
differences
ABM_BM11PAD-IIh-5
Describe the different kinds
of graphs and its essential
parts for data presentation.
Week 8
Give a set of business data;
identify the graphs to be
used
ABM_BM11PAD-IIi-8
Draw the graph/table to
present the data
ABM_BM11PAD-IIi-9
Analyze and interpret the
data presented in a
graph/table
Week 9 ABM_BM11PAD-IIi-10
Use software (i.e., MS Excel,
SPSS) programs to compute
and present graphical
representation of business
data
ABM_BM11PAD-IIj-11

73
Subject: Basic Calculus
Quarter Content
Standards
The learners
demonstrate an
understanding of…
Performance
Standards
The learner shall be
able to…
The learners…
Quarter
3
the basic
concepts of limit
and continuity of
a function
formulate and
solve accurately
real-life problems
involving continuity
of functions
illustrate the limit of a function using a table of values and
the graph of the function
Week 1 STEM_BC11LC-
IIIa-1
distinguish between limxc f(x) and f(c) STEM_BC11LC-
IIIa-2
illustrate the limit laws STEM_BC11LC-
IIIa-3
apply the limit laws in evaluating the limit of algebraic
functions (polynomial, rational, and radical
STEM_BC11LC-
IIIa-4
compute the limits of exponential, logarithmic, and
trigonometric functions using tables ofvalues and graphs of the
functions
Week 2
STEM_BC11LC-
IIIb-1
illustrate limits involving the expressions
and using tables of values
STEM_BC11LC-
IIIb-2
illustrate continuity of a function at a number Week 3 STEM_BC11LC-
IIIc-1
determine whether a function is continuous at a number or
not
STEM_BC11LC-
IIIc-2
illustrate continuity of a function on an interval STEM_BC11LC-
IIIc-3
solves problems involving continuity of a function STEM_BC11LC-
IIId-3
basic concepts
of derivatives
formulate and solve
accurately situational
problems involving
extreme values
illustrate the tangent line to the graph of a function at a given
point
Week 4 STEM_BC11D-
IIIe-1
applies the definition of the derivative of a function at a given
number
STEM_BC11D-
IIIe-2

74
Quarter Content
Standards
The learners
demonstrate an
understanding of…
Performance
Standards
able to…
The learners…
relate the derivative of a function to the slopeof the tangent
line
STEM_BC11D-
IIIe-3
determine the relationship between differentiability and
continuity of afunction Week 5 STEM_BC11D -
IIIf-1
apply the differentiation rules in computing the derivative of an
algebraic, exponential, logarithmic, trigonometric functions and
inverse trigonometric functions
STEM_BC11D-
IIIf-3
illustrate the Extreme Value Theorem Week 6
solve optimization problems that yield polynomial functions
formulate and solve
problems involving
related rates
illustrate the Chain Rule of differentiation STEM_BC11D-
IIIh-2
solve problems using the Chain Rule Week 7
to 8
STEM_BC11D-
IIIh-i-1
illustrate implicit differentiation STEM_BC11D-IIIi-
2
solve problems (including logarithmic, andinverse
trigonometric functions) using implicit differentiation Week 9
STEM_BC11D-
IIIi-j-1
solve situational problems involving related rates STEM_BC11D-IIIj-
2
Quarter
4
antiderivatives
and Riemann
integral
formulate and solve
problems involving
population models
illustrate an antiderivative of a function Week 1
to 3
STEM_BC11I-IVa-
1
compute the general antiderivative of polynomial, radical,
exponential, and trigonometric functions
STEM_BC11I-IVa-
b-1
compute the antiderivative of a function using substitution rule
solve problems involving antidifferentiation Week 4
solve situational problems involving exponential growth and
decay
Week 5
to 6
formulate and solve
accurately real-life
problems involving
illustrate the definite integral as the limit of the Riemann sums
illustrate the Fundamental Theorem of Calculus STEM_BC11I-IVh-
1

75
Quarter Content
Standards
The learners
demonstrate an
understanding of…
Performance
Standards
able to…
The learners…
areas of plane regions compute the definite integral of a functionusing the
Fundamental Theorem of Calculus
Week 7 STEM_BC11I-IVh-
2
compute the definite integral of a functionusing the substitution
rule
STEM_BC11I-IVi-
2
compute the area of a plane region using the definite integral Week 8 STEM_BC11I-IVi-
j-1
solve problems involving areas of plane regions Week 9 STEM_BC11I-IVj-
2
Subject: Pre-Calculus
The learners
demonstrate an
understanding of…
Performance
Standards
The learner shall be able
to…
The learners…
Quarter
1
key concepts of
conic sections and
systems of
nonlinear
equations
model situations
appropriately and solve
problems accurately
using conic sections
and systems of
nonlinear equations
illustrate the different types of conic sections:
parabola, ellipse, circle, hyperbola, and
degenerate cases.
Week 1 STEM_PC11AG-
Ia-1
define a circle. STEM_PC11AG-
Ia-2
determine the standard form of equation of a
circle
STEM_PC11AG-
Ia-3
define a parabola Week 2 STEM_PC11AG-
Ia-5

76
The learners
demonstrate an
understanding of…
Performance
Standards
to…
The learners…
parabola
STEM_PC11AG-
Ib-1
define an ellipse Week 3 STEM_PC11AG-
Ic-1
determine the standard form of equation of an
ellipse
STEM_PC11AG-
Ic-2
define a hyperbola Week 4 STEM_PC11AG-
Id-1
hyperbola
STEM_PC11AG-
Id-2
recognize the equation and important
characteristics of the different types of conic
sections
Week 5 to 6 STEM_PC11AG-
Ie-1
solves situational problems involving conic
sections
STEM_PC11AG-
Ie-2
an understanding
of key concepts of
series and
mathematical
induction and the
Binomial Theorem.
shall be able to keenly
observe and investigate
patterns, and formulate
appropriate
mathematical
statements
Illustrate a series Week 7 to 9 STEM_PC11SMI-
Ih-1
differentiate a series from a sequence STEM_PC11SMI-
Ih-2
use the sigma notation to represent a series STEM_PC11SMI-
Ih-3
Apply the use of sigma notation in finding sums
Quarter
2
an understanding
key concepts of
circular functions,
trigonometric
identities, inverse
1. formulate and solve
problems involving
circular functions
illustrate the unit circle and the relationship
between the linear and angular measures of a
central angle in a unit circle
Week 1 to 2 STEM_PC11T-IIa-
1
convert degree measure to radian measure and
vice versa
STEM_PC11T-IIa-
2

77
The learners
demonstrate an
understanding of…
Performance
Standards
to…
The learners…
trigonometric
functions, and the
polar coordinate
system
illustrate angles in standard position and
coterminal angles
STEM_PC11T-IIa-
3
illustrate the different circular functions Week 3 STEM_PC11T-IIb-
1
uses reference angles to find exact values of
circular functions
STEM_PC11T-IIb-
2
illustrate the domain and range of the different
circular functions
Week 4 STEM_PC11T-IIc-
1
graph the six circular functions (a) amplitude, (b)
period, and (c) phase shift
STEM_PC11T-IIc-
d-1
solve situational problems involving circular
functions
Week 5 STEM_PC11T-IId-
2
2. apply appropriate
trigonometric identities
in solving situational
problems
determine whether an equation is an identity or
a conditional equation
Week 6 to 8 STEM_PC11T-IIe-
1
apply trigonometric identities to find other
trigonometric values
solve situational problems involving
trigonometric identities
STEM_PC11T-IIg-
2
3. formulate and solve
problems involving
appropriate
trigonometric
functions
illustrate the domain and range of the inverse
trigonometric functions.
STEM_PC11T-IIh-
1
evaluate an inverse trigonometric expression. STEM_PC11T-IIh-
2
solve trigonometric equations. STEM_PC11T-IIh-
i-1
solve situational problems involving inverse
trigonometric functions and trigonometric
equations
Week 9 STEM_PC11T-IIi-2

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